Question

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.

Answer 1

Answer: It is a nonlinear function.

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
`=\frac{\text{Change in y}}{\text{Change in x}}`

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

`\frac{\text{Change in y}}{\text{Change in x}}\\\\=(120-60)/(8-2)=(60)/(6)=10`

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

`=(170-120)/(16-8)=(50)/(8)=6.25`

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.

Answer 2

It is a nonlinear function.

Explanation:

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.