Interpretting Functions: Function Notation and Evaluation (CCSS.F-IF.2)
Help Questions
Common Core: High School - Functions › Interpretting Functions: Function Notation and Evaluation (CCSS.F-IF.2)
A music streaming app models total monthly cost by $f(m)=5+2m$, where $m$ is the number of premium add-ons and $f(m)$ is the cost in dollars.
What is the value of $f(3)$?
11
10
6
15
Explanation
Compute $f(3)=5+2(3)=11$. This means the total cost for 3 add-ons is 11 dollars.
A plant's height after $t$ weeks is modeled by $h(t)=12+3t$ (centimeters), where $h(t)$ is the plant's height.
What does $h(5)$ represent?
The number of weeks when the plant is 5 cm tall
The plant's height after 5 weeks
That the plant grows 5 cm each week
The plant's height after 12 weeks
Explanation
$h(5)$ is the height after 5 weeks; numerically, $h(5)=12+3(5)=27$ cm.
The temperature in degrees Fahrenheit is given by $F(c)=1.8c+32$, where $c$ is the temperature in degrees Celsius.
What is the value of $F(10)$?
60
48
50
43.8
Explanation
Compute $F(10)=1.8(10)+32=18+32=50$. This is the Fahrenheit temperature when it is 10°C.
A car rental's total cost in dollars is $C(d)=50+45d$, where $d$ is the number of days.
Which statement best interprets $C(2)=140$?
The cost per day is 140 dollars
After 140 days, the cost is 2 dollars
The starting fee is 140 dollars and each day adds 2 dollars
The total cost for 2 days is 140 dollars
Explanation
Substitute $d=2$: $C(2)=50+45(2)=140$, so the total cost for 2 days is 140 dollars.
A parking garage charges $P(h)$ dollars for $h$ hours: $P(h)=2h+1$ if $h\le 3$, and $P(h)=h^2-1$ if $h>3$.
What is the value of $P(3)$?
7
8
6
10
Explanation
Since $3\le 3$, use the first rule: $P(3)=2(3)+1=7$. This is the charge for 3 hours.
A bakery charges $f(n) = 2.5n + 4$ dollars for an order of $n$ cupcakes.
What is the value of $f(6)$?
12.5
25
19
11
Explanation
Compute $f(6)=2.5(6)+4=15+4=19$, the total cost for 6 cupcakes.
Let $g(t)$ be the distance in miles a runner has traveled $t$ minutes after starting, with $g(t)=0.1t$.
What does $g(30)$ represent?
The distance in miles the runner has traveled after 30 minutes.
The time in minutes when the runner reaches 30 miles.
The runner's speed 30 minutes after starting.
The distance the runner will travel in 0.1 minutes.
Explanation
$g$ takes minutes as input and outputs miles, so $g(30)$ is the miles after 30 minutes (numerically $g(30)=0.1(30)=3$ miles).
For $x$ in the real numbers, $h(x)=x^2-3x+2$.
What is the value of $h(-2)$?
0
-12
4
12
Explanation
$h(-2)=(-2)^2-3(-2)+2=4+6+2=12$.
A reading plan models pages read by $p(n)=50n+20$, where $p(n)$ is the total pages read after $n$ days.
What is the value of $p(3)$?
73
170
1150
130
Explanation
$p(3)=50(3)+20=150+20=170$ pages in total after 3 days.
In a lab, $T(d)$ gives the temperature in degrees Celsius of a solution $d$ minutes after heating begins.
Which statement best describes $T(5)=60$?
After 5 minutes, the solution's temperature is 60 degrees Celsius.
At 60 minutes, the solution's temperature is 5 degrees Celsius.
The temperature increases by 5 degrees every 60 minutes.
It takes 60 minutes for the solution to reach 5 degrees Celsius.
Explanation
$T(5)=60$ means when the input is 5 minutes, the output temperature is 60 degrees Celsius.