Given the function , what is ?
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Algebra Quiz
Practice Function Notation And Evaluation in Algebra with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.
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Given the function f(x)=2x−7, what is f(4)?
This quiz focuses on Function Notation And Evaluation, giving you a quick way to practice the rules, question types, and explanations that matter most for Algebra.
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.
Given the function f(x)=2x−7, what is f(4)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like f(x) = 2x - 7 at a specific value, we replace every x with that value and calculate: f(4) means substitute 4 for x, giving 2(4) - 7 = 8 - 7 = 1. Starting with f(x) = 2x - 7 and finding f(4), we substitute 4 for x everywhere: f(4) = 2(4) - 7. Now we calculate step by step: 2(4) = 8, then 8 - 7 = 1. Choice B is correct because it properly substitutes 4 for x in the function and calculates accurately: 2(4) - 7 = 8 - 7 = 1. Nice work if you got this! Choice A (-15) makes a sign error, possibly calculating -2(4) - 7 instead of 2(4) - 7. Remember to carefully follow the signs given in the function! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
Given q(x)=x−2x2, evaluate q(2).
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like q(x) = x - 2x² at a specific value, we replace every x with that value and calculate: q(2) means substitute 2 for x, giving 2 - 2(2)². Starting with q(x) = x - 2x² and finding q(2), we substitute 2 for x everywhere: q(2) = 2 - 2(2)². Now we calculate step by step: first (2)² = 4, then 2(4) = 8, and finally 2 - 8 = -6. Choice A is correct because it properly substitutes 2 for x in the function and calculates accurately: 2 - 2(2)² = 2 - 2(4) = 2 - 8 = -6. Nice work if you got this! Choice D gives 6, which would result from making a sign error when subtracting, calculating 8 - 2 instead of 2 - 8. Remember, order matters in subtraction! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For this problem, exponents come before multiplication, which comes before subtraction!
If g(x)=x2+3x−4, what is g(−2)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation g(x) tells us the rule for calculating outputs from inputs: when you see g(-2), it means 'substitute -2 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like g(-2), we need to be extra careful with signs! Substituting -2 for x in g(x) = x² + 3x - 4, we get g(-2) = (-2)² + 3(-2) - 4, which equals 4 + (-6) - 4 = 4 - 6 - 4 = -6. Notice how the parentheses around -2 help keep track of the negative! Choice A is correct because it properly substitutes -2 for x in the function and calculates accurately: (-2)² = 4, 3(-2) = -6, so 4 + (-6) - 4 = -6. Nice work if you got this! Choice B gives -14, which results from forgetting that (-2)² = 4 (positive!) and incorrectly calculating it as -4. Remember, a negative number squared is always positive! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write g(-2) = (-2)² + 3(-2) - 4, not g(-2) = -2² + 3(-2) - 4. The parentheses keep everything clear!
If f(x)=4−2x, what does f(5) equal?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like f(x) = 2x + 5 at a specific value, we replace every x with that value and calculate: f(3) means substitute 3 for x, giving 2(3) + 5 = 6 + 5 = 11. Starting with f(x) = 4 - 2x and finding f(5), we substitute 5 for x everywhere: f(5) = 4 - 2(5). Now we calculate step by step: 4 - 10 = -6. Choice B is correct because it properly substitutes 5 for x in the function and calculates accurately: 4 - 2(5) = -6. Nice work if you got this! Choice A is a common slip-up: it makes an order of operations mistake or sign error, perhaps calculating 4 - 2 + 5 or 4 + 2(5) = 14. Remember, subtraction comes after multiplying! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. To check your work, ask yourself: 'Did I replace every single x with my input value?' and 'Did I follow PEMDAS for my calculation?' These two checks catch most mistakes!
For g(x)=−4(x−1), what is g(0)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like g(x)=−4(x−1) at a specific value, we replace every x with that value and calculate: g(0) means substitute 0 for x, giving −4(0−1)=−4(−1)=4. Starting with g(x)=−4(x−1) and finding g(0), we substitute 0 for x everywhere: g(0)=−4(0−1). Now we calculate step by step: 0−1=−1, −4(−1)=4. Choice B is correct because it properly substitutes 0 for x in the function and calculates accurately: −4(−1)=4. Nice work if you got this! Choice A is a common slip-up: it makes a sign error, perhaps forgetting to multiply by -4 or mishandling the negative inside. Remember to follow the order of operations! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x)=3x−2, find f(4) → f(4)=3(4)−2=12−2=10. Easy!
If h(x)=x−3, what is the value of h(0)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like h(x) = x - 3 at a specific value, we replace every x with that value and calculate: h(0) means substitute 0 for x, giving 0 - 3 = -3. Starting with h(x) = x - 3 and finding h(0), we substitute 0 for x everywhere: h(0) = 0 - 3. Now we calculate step by step: -3. Choice B is correct because it properly substitutes 0 for x in the function and calculates accurately: 0 - 3 = -3. Nice work if you got this! Choice C is a common slip-up: it confuses what's being asked: it gives 0 instead of specifically finding h(0) by subtracting 3. Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. Think of a function as a machine: you put in an input (x = 0), the machine follows its rule (x - 3), and out comes an output (-3). The notation f(0) just means 'what does the machine output when I feed it 0?'
If f(x)=10−3x, what is the value of f(4)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(4), it means 'substitute 4 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with f(x) = 10 - 3x and finding f(4), we substitute 4 for x everywhere: f(4) = 10 - 3(4). Now we calculate step by step: 3(4) = 12, 10 - 12 = -2. Choice B is correct because it properly substitutes 4 for x in the function and calculates accurately: 10 - 12 = -2. Nice work if you got this! Choice D is a common slip-up: it has the right idea but makes an order of operations mistake, perhaps calculating 10 - 3 as 7 then multiplying by 4 to get 28, but we should multiply first following PEMDAS. Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
Given f(x)=−2x+6, what does f(−1) equal?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(-1), it means 'substitute -1 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-1), we need to be extra careful with signs! Substituting -1 for x in f(x) = -2x + 6, we get -2(-1) + 6 = 2 + 6 = 8. Notice how the parentheses around -1 help keep track of the negative! Choice B is correct because it properly substitutes -1 for x in the function and calculates accurately: -2(-1) + 6 = 8. Nice work if you got this! Choice C is a common slip-up: it makes a sign error when working with the negative input -1. When you substitute a negative number, use parentheses to keep track: -2(-1) is +2, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!
A plant grows at a steady rate. Its height (in centimeters) after t weeks is H(t)=3t+10. What is H(4)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. In real-world contexts, a function like H(t) = 3t + 10 gives us a formula to calculate one quantity (like height) from another (like weeks), and evaluating H(4) tells us the specific height after 4 weeks. In this problem, H(4)=3(4)+10=12+10=22 centimeters, which means the height after 4 weeks is 22 centimeters. The function helps us quickly answer 'what if' questions by just plugging in different input values! Choice A is correct because it properly substitutes 4 for t in the function and calculates accurately: 3(4)+10=22. Nice work if you got this! Choice C is a common slip-up: it makes an arithmetic error, calculating 3∗4+10 as 12+5 or something similar. Double-checking your arithmetic is always a good idea! In word problems, always state what your answer means: don't just write 'H(4) = 22'—say 'H(4) = 22 centimeters, which is the height after 4 weeks.' This shows you understand what the math represents!
Given s(x)=5x−2, what is the value of s(−4)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like s(x) = 5x - 2 at a specific value, we replace every x with that value and calculate: s(-4) means substitute -4 for x, giving 5(-4) - 2. When evaluating with a negative number like s(-4), we need to be extra careful with signs! Substituting -4 for x in s(x) = 5x - 2, we get s(-4) = 5(-4) - 2, which equals -20 - 2 = -22. Notice how multiplying a positive by a negative gives a negative result! Choice A is correct because it properly substitutes -4 for x in the function and calculates accurately: 5(-4) - 2 = -20 - 2 = -22. Nice work if you got this! Choice D (22) makes a sign error, possibly calculating 5(4) - 2 instead of 5(-4) - 2. Remember that multiplying a positive number by a negative number always gives a negative result! When substituting negative numbers, always use parentheses to protect yourself from sign errors: write s(-4) = 5(-4) - 2. The parentheses keep everything clear! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations.
Given g(x)=x−(2x−1), evaluate g(4).
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation g(x) tells us the rule for calculating outputs from inputs: when you see g(4), it means 'substitute 4 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with g(x)=x−(2x−1) and finding g(4), we substitute 4 for x everywhere: g(4)=4−(2(4)−1). Now we calculate step by step: 2(4)=8, 8−1=7, then 4−7=−3. Choice A is correct because it properly substitutes 4 for x in the function and calculates accurately: 4−7=−3. Nice work if you got this! Choice D is a common slip-up: it has the right idea but makes an order of operations mistake by not evaluating inside the parentheses first, perhaps calculating x - 2x - 1 without the grouping. Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x)=3x−2, find f(4) → f(4)=3(4)−2=12−2=10. Easy!
For f(x)=x2−x, what does f(−3) equal?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(-3), it means 'substitute -3 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-3), we need to be extra careful with signs! Substituting -3 for x in f(x) = x² - x, we get (-3)² - (-3), which equals 9 + 3 = 12. Notice how the parentheses around -3 help keep track of the negative! Choice B is correct because it properly substitutes -3 for x in the function and calculates accurately: 9 + 3 = 12. Nice work if you got this! Choice C is a common slip-up: it makes a sign error when working with the negative input -3, forgetting that - (-3) becomes +3, perhaps calculating 9 - 3 = 6 but with wrong sign. When you substitute a negative number, use parentheses to keep track: (-3)² is positive, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!
If h(x)=x2+2, what is h(0)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like h(x) = x² + 2 at a specific value, we replace every x with that value and calculate: h(0) means substitute 0 for x, giving (0)² + 2 = 0 + 2 = 2. Starting with h(x) = x² + 2 and finding h(0), we substitute 0 for x everywhere: h(0) = (0)² + 2. Now we calculate step by step: 0 + 2 = 2. Choice C is correct because it properly substitutes 0 for x in the function and calculates accurately: 0 + 2 = 2. Nice work if you got this! Choice A is a common slip-up: it confuses what's being asked: it gives 0 instead of adding 2. Remember to complete the calculation! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. Think of a function as a machine: you put in an input (x = 0), the machine follows its rule (x² + 2), and out comes an output (2). The notation f(0) just means 'what does the machine output when I feed it 0?'
For the function f(x)=2x2+1, what is f(−3)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(-3), it means 'substitute -3 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-3), we need to be extra careful with signs! Substituting -3 for x in f(x) = 2x² + 1, we get 2(-3)² + 1 = 2(9) + 1 = 18 + 1 = 19. Notice how the parentheses around -3 help keep track of the negative! Choice B is correct because it properly substitutes -3 for x in the function and calculates accurately: 2(9) + 1 = 19. Nice work if you got this! Choice D is a common slip-up: it makes a sign error when working with the negative input -3. When you substitute a negative number, use parentheses to keep track: (-3)² is positive, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!
Given f(x)=2−5x, what is f(0)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(0), it means 'substitute 0 for every x in the function formula,' like filling in a blank everywhere you see x. Starting with f(x) = 2 - 5x and finding f(0), we substitute 0 for x everywhere: f(0) = 2 - 5(0). Now we calculate step by step: 5(0) = 0, so 2 - 0 = 2. Choice B is correct because it properly substitutes 0 for x in the function and calculates accurately: 2 - 0 = 2. Nice work if you got this! Choice A is a common slip-up: it substitutes correctly but then makes an arithmetic error, calculating 2 - 5(0) as -5 instead of 2. Double-checking your arithmetic is always a good idea! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
If f(x)=x2−1, find both f(3) and f(−3).
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(3), it means 'substitute 3 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-3), we need to be extra careful with signs! Substituting -3 for x in f(x) = x² - 1, we get (-3)² - 1 = 9 - 1 = 8, and for f(3) = (3)² - 1 = 9 - 1 = 8. Notice how the parentheses around -3 help keep track of the negative! Choice B is correct because it properly substitutes 3 and -3 for x in the function and calculates accurately: both give 8. Nice work if you got this! Choice A is a common slip-up: it makes a sign error when working with the negative input -3. When you substitute a negative number, use parentheses to keep track: (-3)² is positive, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!
For the function f(x)=3x−7, evaluate f(−2).
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. Function notation f(x) tells us the rule for calculating outputs from inputs: when you see f(-2), it means 'substitute -2 for every x in the function formula,' like filling in a blank everywhere you see x. When evaluating with a negative number like f(-2), we need to be extra careful with signs! Substituting -2 for x in f(x) = 3x - 7, we get 3(-2) - 7, which equals -6 - 7 = -13. Notice how the parentheses around -2 help keep track of the negative! Choice C is correct because it properly substitutes -2 for x in the function and calculates accurately: 3(-2) - 7 = -13. Nice work if you got this! Choice B is a common slip-up: it makes a sign error when working with the negative input -2. When you substitute a negative number, use parentheses to keep track: 3(-2) is -6, but forgetting parentheses can lead to the wrong sign. When substituting negative numbers, always use parentheses to protect yourself from sign errors: write f(-3) = 2(-3)² + 1, not f(-3) = 2-3² + 1. The parentheses keep everything clear!
For g(x)=2(x+4), what is g(−4)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like g(x) = 2(x + 4) at a specific value, we replace every x with that value and calculate: g(-4) means substitute -4 for x, giving 2(-4 + 4) = 2(0) = 0. Starting with g(x) = 2(x + 4) and finding g(-4), we substitute -4 for x everywhere: g(-4) = 2(-4 + 4). Now we calculate step by step: -4 + 4 = 0, then 20 = 0. Choice B is correct because it properly substitutes -4 for x in the function and calculates accurately: 2(0) = 0. Nice work if you got this! Choice A is a common slip-up: it has the right idea but makes an order of operations mistake: it calculates 2(-4) + 4 instead of grouping (x + 4) first. Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x) = 3x - 2, find f(4) → f(4) = 3(4) - 2 = 12 - 2 = 10. Easy!
Given the function f(x)=2x+5, what is f(3)?
Explanation: This question tests your understanding of function notation and how to evaluate functions by substituting input values. To evaluate a function like f(x)=2x+5 at a specific value, we replace every x with that value and calculate: f(3) means substitute 3 for x, giving 2(3)+5=6+5=11. Starting with f(x)=2x+5 and finding f(3), we substitute 3 for x everywhere: f(3)=2(3)+5. Now we calculate step by step: 6+5=11. Choice B is correct because it properly substitutes 3 for x in the function and calculates accurately: 2(3)+5=11. Nice work if you got this! Choice A is a common slip-up: it treats the expression as 2∗(3+5) instead of 2∗3+5, forgetting order of operations. Remember, multiplication before addition! Here's the foolproof way to evaluate functions: (1) write out the function formula, (2) wherever you see the variable, write the input value in parentheses, (3) calculate step by step using order of operations. For example: f(x)=3x−2, find f(4) → f(4)=3(4)−2=12−2=10. Easy!
For the function r(x)={2x+1−x+4if x≥0if x<0, what is r(−2)?
Explanation: This question tests your understanding of function notation and how to evaluate piecewise functions by choosing the correct rule based on the input value. Function notation r(x) tells us the rule for calculating outputs from inputs, but this function has two different rules depending on whether x is negative or non-negative. For r(-2), since -2 < 0, we use the second rule: r(x) = -x + 4. Substituting -2 for x, we get r(-2) = -(-2) + 4 = 2 + 4 = 6. Choice C is correct because it properly identifies that -2 < 0, uses the correct rule -x + 4, and calculates accurately: -(-2) + 4 = 2 + 4 = 6. Nice work if you got this! Choice A (-3) might come from using the wrong rule (2x + 1) with x = -2, giving 2(-2) + 1 = -4 + 1 = -3. Remember to check which condition your input satisfies before choosing the rule! Think of a piecewise function as a machine with different settings: you first check which setting to use (is x < 0?), then apply that specific rule. The notation tells you exactly which formula to use based on your input value. To evaluate piecewise functions: (1) check which condition your input satisfies, (2) use only that rule, (3) substitute and calculate carefully. Always double-check you're using the right piece!