Comparing Function Values

4.3.1 Comparing Function Values

4.3.1 • Comparing Function Values

Warm Up

A black quadcopter drone with a camera hovers in mid-air over a blurred field and trees under a clear blue sky.

Here is a graph that represents function $f$ , which gives the height of a drone, in meters, $t$ seconds after it leaves the ground.

A line graph shows height (meters) vs. time (seconds). The height rises from 0 to 4 meters between 0-2 seconds, stays at 4 meters until 5 seconds, then drops back to 0 meters by 7 seconds.

Decide which function value is greater: $f (0)$ or $f (4)$

$f (4)$

Explain your thinking as to which is greater, $f (0)$ or $f (4)$ , or if they are equal.

Compare your answer: Your answer may vary, but here is a sample. The output value at f(4) is greater than the output value at f(0) because at 4 seconds the drone is 4 meters off the ground while at 0 seconds, the drone is on the ground (0 meters).

Decide which function value is greater: $f (2)$ or $f (5)$ , or if they are equal.

They are equal.

Explain your thinking as to which is greater, $f (2)$ or $f (5)$ , or if they are equal.

Compare your answer: Your answer may vary, but here is a sample. The output value at f(2) is equal to the output value at f(5) because at both 2 seconds and 5 seconds, the drone is 4 meters off the ground.

Decide which function value is greater, $f (3)$ or $f (7)$ , or if they are equal.

$f (3)$

Explain your thinking as to which is greater, $f (3)$ or $f (7)$ , or if they are equal.

Compare your answer: Your answer may vary, but here is a sample. The output value at f(3) is greater than the output value at f(7) because at 3 seconds the drone is 4 meters off the ground while at 7 seconds, the drone is on the ground (0 meters).

Decide which function value is greater, $f (t)$ or $f (t + 1)$ , or if they are equal.

It depends on the value of $t$ .

Explain your thinking as to which is greater, $f (t)$ or $f (t + 1)$ , or if they are equal.

Compare your answer: Your answer may vary, but here are some samples.

It depends on the value of t because during some time periods the values of the function are equal.
It depends on the value of t because between 0-2 seconds, f(t+1) is greater than f(t) but it is exactly the opposite between 5-7 seconds where f(t) is greater.
It depends on the value of t because between 0-2 seconds, f(t+1) is greater, between 2-5 seconds the values are equal, and after 5 seconds, f(t) is greater.