Question

function $f$ gives the distance of a runner from the starting line $t$ seconds after the race begins. distance is measured in meters. the graph below represents $f$. (graph shows: the runner starts at 0 meters, moves away steadily, stops for a short time, moves further away, then returns back to 0 meters by the end.) select all statements in function notation that represent the situation. a. $f(20) = 40$ b. $f(80) = f(40)$ c. $f(0) = 60$ d. $f(150) < f(100)$ e. $f(170) = 0$ (3 choices)

Explanation:

Step1: Check Option A

At $t=20$, the graph shows distance = 40. So $f(20)=40$ is true.

Step2: Check Option B

At $t=80$ and $t=40$, distance is 40. So $f(80)=f(40)$ is true.

Step3: Check Option C

At $t=0$, distance is 0, not 60. So $f(0)=60$ is false.

Step4: Check Option D

At $t=150$, distance = 60; at $t=100$, distance < 60. So $f(150) < f(100)$ is false.

Step5: Check Option E

At $t=170$, distance approaches 0, and $t=180$ is 0. So $f(170)=0$ is true.

Answer:

A. $f(20) = 40$
B. $f(80) = f(40)$
E. $f(170) = 0$