Math 1 Quiz: Evaluating And Interpreting Functions
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Evaluating And Interpreting FunctionsQuestion 1 of 20

A water treatment plant's filtration rate can be modeled by the function F(t) = 850 - 45t + 2.5t², where F(t) represents the filtration rate in gallons per minute and t represents the number of hours since the last filter cleaning (0 ≤ t ≤ 12).

What is the practical meaning of F(6) = 775 in this context?

After 6 hours, the plant filters water at a rate of 775 gallons per minute
The plant filters a total of 775 gallons during the first 6 hours of operation
The filtration rate increases by 775 gallons per minute every 6 hours of operation
The plant requires 775 minutes to filter water after 6 hours since cleaning
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Math 1 Quiz

Math 1 Quiz: Evaluating And Interpreting Functions

Practice Evaluating And Interpreting Functions in Math 1 with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Evaluating And Interpreting Functions, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 1.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A water treatment plant's filtration rate can be modeled by the function F(t) = 850 - 45t + 2.5t², where F(t) represents the filtration rate in gallons per minute and t represents the number of hours since the last filter cleaning (0 ≤ t ≤ 12).

What is the practical meaning of F(6) = 775 in this context?

  1. After 6 hours, the plant filters water at a rate of 775 gallons per minute (correct answer)
  2. The plant filters a total of 775 gallons during the first 6 hours of operation
  3. The filtration rate increases by 775 gallons per minute every 6 hours of operation
  4. The plant requires 775 minutes to filter water after 6 hours since cleaning
Explanation: F(6) = 775 means that when t = 6 (6 hours since the last filter cleaning), the filtration rate F(t) equals 775 gallons per minute. Since F(t) represents the rate of filtration, F(6) tells us the instantaneous rate at that specific time point. Choice B confuses rate with total volume. Choice C misinterprets this as a rate of change. Choice D incorrectly interprets the output as time rather than rate.

Question 2

The temperature inside a greenhouse is modeled by T(h) = 68 + 12sin(πh/12), where T(h) is the temperature in degrees Fahrenheit and h is the number of hours after midnight.

If T(15) = 62, what does this tell us about the greenhouse conditions?

  1. At 3:00 PM, the greenhouse temperature is 62°F, which is below the base temperature (correct answer)
  2. The greenhouse reaches its minimum temperature of 62°F exactly 15 minutes after midnight
  3. The greenhouse temperature drops by 62 degrees during the 15-hour period after midnight
  4. The greenhouse maintains a constant temperature of 62°F for 15 consecutive hours daily
Explanation: T(15) = 62 means that 15 hours after midnight (3:00 PM), the temperature is 62°F. Since the base temperature is 68°F (the constant term), this represents a temperature below the baseline. Choice B confuses hours with minutes and misidentifies when the minimum occurs. Choice C incorrectly interprets the function value as a change in temperature rather than the actual temperature. Choice D misunderstands the function as representing a constant temperature over time.

Question 3

The height of a projectile is given by h(t) = -16t² + 64t + 80, where h(t) is the height in feet and t is the time in seconds after launch.

Given that h(2.5) = 100, what does this indicate about the projectile's motion?

  1. The projectile reaches its maximum height of 100 feet exactly 2.5 seconds after launch
  2. At 2.5 seconds after launch, the projectile is at a height of 100 feet above ground (correct answer)
  3. The projectile travels 100 feet horizontally during the first 2.5 seconds of flight
  4. The projectile's velocity is 100 feet per second when it has been airborne for 2.5 seconds
Explanation: h(2.5) = 100 simply means that at t = 2.5 seconds, the height is 100 feet. This is a direct evaluation of the position function. Choice A incorrectly assumes this is the maximum height without finding where h'(t) = 0. Choice C confuses vertical height with horizontal distance. Choice D misinterprets the height function value as velocity, which would require taking the derivative.

Question 4

A cell phone plan charges according to the function C(m) = 45 + 0.15(m - 500) for m > 500, where C(m) is the monthly cost in dollars and m is the number of minutes used. What is the meaning of C(750) = 82.50?

  1. Using 750 minutes costs $82.50, with $37.50 in overage charges beyond the base plan (correct answer)
  2. The monthly bill is $82.50 when exactly 750 minutes are included in the base plan
  3. Each minute over 750 costs $82.50, making this the premium rate threshold
  4. The plan allows 750 minutes before charging the additional $82.50 monthly fee
Explanation: C(750) = 82.50 means using 750 minutes results in a total cost of $82.50. The base cost is $45, and the overage charge is 0.15(750-500) = 0.15(250) = $37.50, giving 45 + 37.50 = $82.50. Choice B misunderstands the function structure - 500 minutes are included in the base plan, not 750. Choice C incorrectly interprets the total cost as the per-minute rate. Choice D misrepresents how the billing structure works.

Question 5

The number of subscribers to a streaming service is modeled by S(m) = 2000(1.15)^m, where S(m) is the number of subscribers and m is the number of months since launch.

If S(6) ≈ 4626, what does this indicate about the service's growth?

  1. The service gains 4626 new subscribers during month 6
  2. The service needs 4626 months to reach 6 subscribers
  3. The service's growth rate is 4626 subscribers per month
  4. After 6 months, the service has approximately 4626 subscribers (correct answer)
Explanation: When you encounter an exponential growth model like S(m)=2000(1.15)mS(m) = 2000(1.15)^m, you're looking at a function that describes cumulative values over time. The key insight is understanding what the output represents when you plug in a specific input value. The function S(m)S(m) gives you the total number of subscribers after mm months. When we calculate S(6)≈4626S(6) ≈ 4626, we're finding the total subscriber count at the 6-month mark. This means after 6 months have passed since launch, the streaming service has approximately 4626 total subscribers. Choice D correctly interprets this relationship between input (6 months) and output (4626 total subscribers). Choice A misinterprets the function output as new subscribers gained during month 6, rather than the cumulative total. The 4626 represents all subscribers, not just new additions in that specific month. Choice B confuses the input and output variables entirely, suggesting months are needed to reach a subscriber count, when the function actually uses months as input to find total subscribers. Choice C treats the output as a growth rate (subscribers per month), but 4626 is the total count at a point in time, not a rate of change. The growth rate would come from the base 1.15, indicating 15% monthly growth. Remember: with exponential functions modeling real-world scenarios, always check whether the output represents a cumulative total, a rate, or an incremental change. The function notation and context will guide you to the correct interpretation.

Question 6

A reservoir's water level is modeled by L(d) = 45 + 8cos(2πd/365), where L(d) is the water level in feet above sea level and d is the number of days since January 1st.

If L(91) ≈ 37, what does this indicate about the reservoir conditions?

  1. The water level changes by 37 feet every 91 days throughout the year
  2. The reservoir loses 37 feet of water during the first 91 days of the year
  3. The minimum possible water level of 37 feet occurs 91 days after January 1st
  4. On approximately April 1st, the water level is about 37 feet, which is below average (correct answer)
Explanation: When you encounter a sinusoidal function modeling real-world data, focus on interpreting what specific function values mean in context rather than just manipulating the formula. Let's evaluate what L(91) ≈ 37 tells us. The function L(d) = 45 + 8cos(2πd/365) has a baseline (average) water level of 45 feet, since that's the vertical shift. The cosine function oscillates between -1 and 1, so the water level varies between 45 - 8 = 37 feet (minimum) and 45 + 8 = 53 feet (maximum). Since L(91) ≈ 37, this means that 91 days after January 1st (which is approximately April 1st), the water level is about 37 feet above sea level. This is 8 feet below the average of 45 feet, confirming it's a below-average water level. Choice A incorrectly suggests the water level changes by 37 feet every 91 days, but 37 is the actual water level, not a rate of change. Choice B misinterprets this as a loss of 37 feet, when 37 feet is the total height above sea level. Choice C claims 37 feet is the minimum occurring at day 91, but while 37 is indeed the minimum possible level, we can't conclude from this single data point that the minimum occurs exactly on day 91. Choice D correctly interprets all the information: the date (April 1st), the water level (37 feet), and that this is below the 45-foot average. Study tip: With sinusoidal models, always identify the baseline value first, then interpret specific outputs as positions relative to that baseline.

Question 7

A city's air quality index is modeled by A(h) = 50 + 25sin(πh/12) + 10cos(πh/6), where A(h) is the air quality index and h is the hour of the day (0 ≤ h ≤ 24).

If A(18) = 45, what does this tell us about the air quality conditions?

  1. Air quality improves by 45 units over 18 hours
  2. Air quality reaches its daily minimum at 6:00 PM
  3. At 6:00 PM, the air quality index is 45 (correct answer)
  4. The city has 45 hours of good air quality per day
Explanation: When you encounter a function notation like A(18) = 45, you're being asked to interpret what happens when you substitute a specific input value into the function. Here, A(h) represents the air quality index at hour h, where h = 0 corresponds to midnight. The equation A(18) = 45 means that when h = 18 (which is 6:00 PM in 24-hour time), the air quality index equals 45. This is a direct substitution and evaluation - nothing more complex than reading the function's output at a specific time. Let's examine why the other answers miss the mark. Answer A incorrectly suggests that 45 represents a change or improvement over time, but A(18) = 45 tells us the index value at one specific moment, not a change. Answer B claims this represents a daily minimum, but we'd need to analyze the entire function using calculus or compare multiple values to determine minimums - we can't conclude this from a single data point. Answer D misinterprets both the number 45 (treating it as hours instead of an index value) and what the equation tells us. The correct answer is C: at 6:00 PM, the air quality index is 45. This directly translates the mathematical statement A(18) = 45 into plain English. Study tip: When you see function notation like f(a) = b, always remember this format means "when the input is a, the output is b." Don't overthink it - focus on the direct relationship between input and output values.

Question 8

The power output of a wind turbine is modeled by P(v) = 0.5v³ for wind speeds between 3 and 25 mph, where P(v) is power in kilowatts and v is wind speed in mph.

Given that P(12) = 864, what does this tell us about the turbine's performance?

  1. Wind speed increases by 864 mph at 12 kilowatts output
  2. Maximum power output of 864 kilowatts occurs at 12 mph
  3. The turbine requires 864 hours to generate 12 kilowatts
  4. The turbine generates 864 kilowatts at 12 mph wind speed (correct answer)
Explanation: When you encounter a function notation problem, focus on understanding what the input and output represent. Here, P(v) represents the power output (in kilowatts) for a given wind speed v (in mph). The notation P(12) = 864 means that when the wind speed is 12 mph (the input), the power output is 864 kilowatts (the output). You can verify this using the given formula: P(12)=0.5(12)3=0.5×1728=864P(12) = 0.5(12)^3 = 0.5 \times 1728 = 864 kilowatts. This directly tells us the turbine generates 864 kilowatts when wind speed is 12 mph. Looking at the wrong answers: Choice A confuses input and output variables, incorrectly suggesting wind speed increases by the power value. Choice B incorrectly assumes this is the maximum power output – but since power increases with the cube of wind speed, higher speeds (up to 25 mph) would produce more power. Choice C introduces an irrelevant time component (hours) that doesn't appear in our power function at all. The key insight is that P(12) = 864 is a single point on the power curve, not information about maximums, time, or variable relationships. Choice D correctly interprets this as the power output at a specific wind speed. Remember: In function notation f(x) = y, x is always the input and y is always the output. Don't let answer choices that flip or confuse these relationships trick you – always identify what goes in and what comes out of the function.

Question 9

The function P(x) = -0.02x² + 8x - 200 models the daily profit in dollars for a bakery when x represents the number of specialty cakes sold. If P(150) = 400, which statement best describes this result?

  1. The bakery's maximum possible profit is $400 when selling 150 specialty cakes daily
  2. Selling 150 specialty cakes results in a daily profit of $400 for the bakery (correct answer)
  3. The bakery needs to sell 400 specialty cakes to achieve a profit of $150
  4. The bakery's profit increases by $400 for every 150 additional specialty cakes sold
Explanation: P(150) = 400 means when x = 150 (150 specialty cakes sold), the profit P(x) = $400. This is a direct function evaluation showing the profit at that specific production level. Choice A incorrectly assumes this is the maximum profit without verification. Choice C reverses the input and output values. Choice D misinterprets the function value as a rate of change rather than the actual profit at x = 150.

Question 10

A company's revenue function is R(x) = 120x - 0.5x², where x represents the number of units sold (in thousands) and R(x) represents revenue in thousands of dollars.

If R(80) = 6400, what is the correct interpretation of this result in the business context?

  1. Selling 80,000 units generates $6,400,000 in revenue for the company (correct answer)
  2. The company's profit is $6,400 when exactly 80 units are manufactured
  3. Each of the 80,000 units sold contributes $6,400 to the total revenue
  4. The company needs $6,400,000 in startup costs to sell 80,000 units
Explanation: Since x is in thousands of units and R(x) is in thousands of dollars, R(80) = 6400 means 80,000 units generate 6,400,000 dollars in revenue. Choice B confuses revenue with profit and ignores the scaling (thousands). Choice C incorrectly suggests each unit contributes $6,400 when the actual revenue per unit would be much less. Choice D misinterprets revenue as startup costs.

Question 11

The function C(n)=45n+120C(n) = 45n + 120 represents the total cost in dollars for a catering company to serve nn people at an event. If C(75)=3495C(75) = 3495, what does this tell us about the catering situation?

  1. The company charges $3495 per person when serving exactly 75 guests
  2. Serving 75 people costs $3495 total, including a $120 setup fee (correct answer)
  3. The company's profit is $3495 when catering for 75 people
  4. Each person pays $3495 divided among 75 guests for the event
Explanation: The function C(n) = 45n + 120 shows a cost structure with $45 per person plus a fixed $120 fee. When C(75) = 3495, this means serving 75 people costs $3495 total. The $120 represents the setup fee (the y-intercept). Choice A incorrectly states the per-person cost as $3495. Choice C confuses cost with profit. Choice D misinterprets how the total cost is structured.

Question 12

A water tank is being drained for maintenance. The function h(t)=250−15t+0.5t2h(t) = 250 - 15t + 0.5t^2 models the height of water in the tank (in centimeters) after tt minutes of draining. What is the practical meaning of h(8)=202h(8) = 202?

  1. After 8 minutes, the water level is 202 cm above the tank bottom (correct answer)
  2. The water level decreases by 202 cm during the first 8 minutes
  3. At 202 minutes, the water level will be 8 cm above the bottom
  4. The tank holds 202 liters of water when drained for 8 minutes
Explanation: The function h(t) represents the height of water at time t. Therefore, h(8) = 202 means that after 8 minutes of draining, the water height is 202 centimeters above the bottom of the tank. Choice B incorrectly interprets this as a change in height rather than the actual height. Choice C switches the input and output values. Choice D incorrectly changes the units from centimeters to liters.

Question 13

A marine biologist is studying water pressure at various depths in the ocean. The pressure function P(d)=14.7+0.445dP(d) = 14.7 + 0.445d gives the total pressure in pounds per square inch (psi) at a depth of dd feet below sea level.

If P(80)=50.3P(80) = 50.3, what does this measurement indicate about the underwater environment?

  1. Water pressure increases by 50.3 psi for every 80 feet of depth
  2. The pressure differential between surface and 80 feet is 50.3 psi
  3. Sea level pressure is 80 psi, increasing to 50.3 psi underwater
  4. At 80 feet below sea level, the total water pressure is 50.3 psi (correct answer)
Explanation: When you encounter function notation like P(80)=50.3P(80) = 50.3, you're looking at an input-output relationship. The function P(d)=14.7+0.445dP(d) = 14.7 + 0.445d models pressure at depth dd, so P(80)P(80) means "the pressure when the depth is 80 feet." Let's verify this makes sense: P(80)=14.7+0.445(80)=14.7+35.6=50.3P(80) = 14.7 + 0.445(80) = 14.7 + 35.6 = 50.3. The calculation confirms that at 80 feet below sea level, the total pressure is 50.3 psi. This is exactly what answer choice D states. Now let's examine why the other choices are incorrect. Choice A misinterprets the relationship—it suggests 50.3 psi is the rate of increase per 80 feet, but 50.3 is the total pressure at that depth, not a rate. Choice B incorrectly identifies 50.3 as just the pressure difference. While the pressure difference between surface (14.7 psi) and 80 feet is indeed 35.6 psi, the 50.3 represents total pressure, not just the difference. Choice C completely reverses the scenario, incorrectly stating that sea level pressure is 80 psi when it's actually 14.7 psi (the constant term in the function). Study tip: With function notation f(x)=yf(x) = y, always remember that yy represents the output value when xx is the input. Don't confuse the output with rates of change, differences, or other relationships—focus on what the function is designed to calculate.

Question 14

A spring's compression distance follows d(F)=0.08F+1.2d(F) = 0.08F + 1.2 centimeters when force FF newtons is applied. If d(15)=2.4d(15) = 2.4, what does this measurement tell us about the spring's behavior?

  1. The spring compresses 2.4 cm total when 15 newtons of force is applied (correct answer)
  2. A force of 2.4 newtons compresses the spring by 15 centimeters total
  3. The spring's compression rate is 2.4 cm per newton up to 15 newtons
  4. Maximum compression is 15 cm when 2.4 newtons of force is applied
Explanation: The function d(F) gives compression distance as a function of applied force, so d(15) = 2.4 means applying 15 newtons compresses the spring 2.4 cm total. This includes the initial compression of 1.2 cm (y-intercept) plus additional compression from the applied force. Choice B switches the input and output values. Choice C misinterprets the total compression as the compression rate. Choice D reverses the force and distance values and mentions maximum compression incorrectly.

Question 15

A projectile's height is modeled by h(t)=−16t2+64t+80h(t) = -16t^2 + 64t + 80 where hh is height in feet and tt is time in seconds after launch. Given that h(1.5)=140h(1.5) = 140, what does this value represent in the context of the projectile's motion?

  1. The projectile reaches its maximum height of 140 feet at 1.5 seconds
  2. At 1.5 seconds after launch, the projectile is 140 feet above ground (correct answer)
  3. The projectile travels 140 feet horizontally in the first 1.5 seconds
  4. The projectile's velocity is 140 feet per second at t = 1.5 seconds
Explanation: The function h(t) represents height at time t, so h(1.5) = 140 means that 1.5 seconds after launch, the projectile is 140 feet above the ground. Choice A incorrectly assumes this is the maximum height without verification. Choice C confuses height with horizontal distance. Choice D confuses the height function with velocity (which would be the derivative).

Question 16

The concentration of a medication in the bloodstream is modeled by C(t)=20tt2+4C(t) = \frac{20t}{t^2 + 4} mg/L, where tt is hours after administration. If C(2)=2.5C(2) = 2.5, what is the medical significance of this result?

  1. The medication concentration peaks at 2.5 mg/L exactly 2 hours after dosing
  2. Patients should take 2.5 mg doses every 2 hours for effectiveness
  3. The medication's half-life is 2.5 hours, reaching 2 mg/L concentration
  4. Two hours after taking the medication, the concentration is 2.5 mg/L (correct answer)
Explanation: When you encounter a function modeling a real-world scenario, focus on what the function's output represents at specific input values. Here, C(t)=20tt2+4C(t) = \frac{20t}{t^2 + 4} gives the concentration in mg/L at time tt hours. Let's verify the calculation: C(2)=20(2)22+4=404+4=408=5C(2) = \frac{20(2)}{2^2 + 4} = \frac{40}{4 + 4} = \frac{40}{8} = 5. Wait - this gives us 5 mg/L, not 2.5 mg/L as stated in the problem. The question appears to contain an error, but we'll work with the given information that C(2)=2.5C(2) = 2.5. The correct interpretation is answer D: this simply means that two hours after administration, the medication concentration in the bloodstream is 2.5 mg/L. This is a direct reading of what the function value represents. A is wrong because knowing one point doesn't tell us where the peak occurs - we'd need to find where C′(t)=0C'(t) = 0 to locate the maximum. B misinterprets the function output as dosing instructions, but 2.5 mg/L is a concentration, not a dose amount. C confuses the concept of half-life (the time for concentration to drop to half its peak value) with a single data point. Remember: when interpreting mathematical models, always connect the function's output back to its real-world meaning. Don't overthink - sometimes the question is asking for the most straightforward interpretation of what a function value represents in context.

Question 17

A car rental company charges according to the function R(m)=89+0.15(m−100)R(m) = 89 + 0.15(m - 100) for m≥100m \geq 100 miles driven, where RR is the total rental cost in dollars. If R(250)=111.50R(250) = 111.50, what does this calculation reveal about the rental agreement?

  1. Driving 250 miles costs $111.50 total, with free mileage up to 100 miles (correct answer)
  2. The rental rate increases to $111.50 per mile after driving 250 miles
  3. Customers pay $250 upfront plus $111.50 for each mile over 100
  4. The company charges $111.50 per day for unlimited mileage up to 250 miles
Explanation: The function R(m) = 89 + 0.15(m - 100) shows a base fee of $89 plus $0.15 for each mile over 100. When R(250) = 111.50, this means driving 250 miles costs $111.50 total, which includes the first 100 miles in the base fee. Choice B misinterprets the total cost as a per-mile rate. Choice C reverses the base fee and mileage structure. Choice D incorrectly describes this as a daily rate with unlimited mileage.

Question 18

The function N(t) = 500 + 200t - 10t² models the number of bacteria in a culture, where t is time in hours. What does N(8) = 1140 tell us about the bacterial population?

  1. The bacteria population peaks at 1140 organisms exactly 8 hours after the experiment begins
  2. After 8 hours, there are 1140 bacteria in the culture, representing continued growth (correct answer)
  3. The bacterial growth rate is 1140 organisms per hour when t = 8 hours
  4. The culture produces 1140 new bacteria during the 8th hour of observation
Explanation: N(8) = 1140 means at t = 8 hours, the population is 1140 bacteria. Since N(0) = 500, this shows growth from the initial population. Choice A incorrectly assumes this is the maximum without checking the derivative. Choice C confuses the population value with the growth rate. Choice D misinterprets the function value as the change during the 8th hour rather than the total population at t = 8.

Question 19

A spring's displacement from equilibrium is given by d(t) = 6cos(4πt), where d(t) is displacement in inches and t is time in seconds. If d(0.125) = 0, what does this represent?

  1. The spring reaches maximum displacement at t = 0.125 seconds
  2. The spring stops oscillating permanently after 0.125 seconds
  3. The spring is at equilibrium position at t = 0.125 seconds (correct answer)
  4. The spring completes 0.125 full oscillations before stopping
Explanation: When you encounter a trigonometric function describing periodic motion like springs, remember that the function value tells you the object's position relative to equilibrium. Here, d(t)=6cos⁡(4πt)d(t) = 6\cos(4\pi t) describes displacement from the spring's natural resting position. Let's verify what happens at t=0.125t = 0.125 seconds by substituting into the equation: d(0.125)=6cos⁡(4π⋅0.125)=6cos⁡(0.5π)=6cos⁡(90°)=6⋅0=0d(0.125) = 6\cos(4\pi \cdot 0.125) = 6\cos(0.5\pi) = 6\cos(90°) = 6 \cdot 0 = 0 Since d(0.125)=0d(0.125) = 0, the displacement is zero inches from equilibrium, meaning the spring is exactly at its equilibrium position at this moment. Answer A is incorrect because maximum displacement occurs when the cosine function equals ±1, giving d=±6d = ±6 inches, not zero. Answer B misunderstands oscillatory motion—springs don't permanently stop oscillating at specific times unless an external force acts on them. The zero displacement is just one point in the continuous cycle. Answer D confuses displacement with the number of completed cycles. To find complete oscillations, you'd need to determine the period and see how many full periods fit into 0.125 seconds. When analyzing periodic motion functions, always remember: zero displacement means the object is at equilibrium, maximum absolute values of the function represent extreme positions, and the motion continues cyclically unless stated otherwise. Focus on what the function value itself represents rather than getting distracted by the time variable.

Question 20

The efficiency of a solar panel is given by E(T) = 0.25 - 0.004(T - 25), where E(T) is efficiency as a decimal and T is temperature in degrees Celsius. What does E(35) = 0.21 mean?

  1. Maximum efficiency of 21% occurs at exactly 35°C
  2. The panel loses 0.21% efficiency for every degree above 35°C
  3. At 35°C, the solar panel operates at 21% efficiency (correct answer)
  4. The panel generates 0.21 kilowatts of power at 35°C
Explanation: When you encounter a function like E(T) and are asked to interpret a specific value like E(35) = 0.21, you're being tested on function interpretation rather than calculation. The key is understanding what the function represents and what the output value means in context. Let's verify the calculation first: E(35)=0.25−0.004(35−25)=0.25−0.004(10)=0.25−0.04=0.21E(35) = 0.25 - 0.004(35 - 25) = 0.25 - 0.004(10) = 0.25 - 0.04 = 0.21. Since efficiency is given "as a decimal," 0.21 means 21% efficiency. This confirms that at 35°C, the solar panel operates at 21% efficiency, making C correct. Now let's examine why the other options are wrong. Option A claims 21% is the maximum efficiency and occurs at exactly 35°C. However, looking at the function, maximum efficiency occurs when the subtracted term is smallest (at T = 25°C), giving E(25) = 0.25 or 25%. Option B misinterprets what 0.21 represents—it's the efficiency at 35°C, not a rate of efficiency loss. The actual rate of efficiency loss is 0.004 (or 0.4%) per degree above 25°C. Option D incorrectly interprets efficiency as power output. Efficiency is a percentage showing how well the panel converts sunlight to electricity, not a measure of actual power generation. Remember: when interpreting function values, always connect the output back to what the function represents. Here, E(T) gives efficiency as a decimal, so E(35) = 0.21 simply means the panel is 21% efficient at that temperature.