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.

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 $=\dfrac{\text{Change in y}}{\text{Change in x}}$

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

$\dfrac{\text{Change in y}}{\text{Change in x}}\\\\=\dfrac{120-60}{8-2}=\dfrac{60}{6}=10$

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

$=\dfrac{170-120}{16-8}=\dfrac{50}{8}=6.25$

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

Answer:

It is a nonlinear function.

Step-by-step 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.