Sully is driving a race car in a race. The table gives the speeds recorded by the speedometer on Sully's car with respect to time.

x
(seconds)

y
(mph)
x y
2 60
8 120
16 170

What type of function is the function representing Sully's speed?

It is a constant function.
It is a linear function.
It is a nonlinear function.
It is a decreasing function.

When the points are graphed, they do not all lie on the same line. The lines connecting the points have positive slope, so the function is neither constant nor decreasing.

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-11-26T07:48:25+01:00

Answer: It is a nonlinear function.

Step-by-step explanation:

A function is said to be linear if the rate of change of dependent varaible (y) with respect to independent variable (x) is constant.

Rate of change in function [tex]=\dfrac{\text{Change in y}}{\text{Change in x}}[/tex]

The table gives the speeds recorded by the speedometer on Sully's car with respect to time. :

x y

(seconds) (mph)

2 60

8 120

16 170

For x= 2 and x= 8 , the rate of change in function will be

[tex]\dfrac{\text{Change in y}}{\text{Change in x}}\\\\=\dfrac{120-60}{8-2}=\dfrac{60}{6}=10[/tex]

For x= 8 and x= 16 , the rate of change in function will be

[tex]=\dfrac{170-120}{16-8}=\dfrac{50}{8}=6.25[/tex]

But 10 ≠ 6.25.

⇒ Rate of change is not constant.

It means the function non- linear.

Also , it is not a constant function because values of y is not constant w.r.t to x.

It is not a decreasing function because values of y increase with increase in x.