Question

The table below represents the velocity of a car as a function of time:

Answer 1

A)The y-intercept is 50 because when X=0, y=50. This shows that the car was moving at 50 mph as an initial speed.

B) in two hours (from 1 to 3) the speed increased by 4 miles per 2hours. (from 52 to 56). 4/2 = 2 mph, which is the average rate of change. This represents the amount of speed increased each hour.

C) y=2x+50, and y=60 in this case, so 60=2x+50
60=2x+50
-50 -50
-----------------
10=2x
5=x, so the domain is X<=5 (less than or equal to 5)

Answer 2

Answer:

Part A: The y-intercept of the function is 50. It means the initial velocity is 50 miles/hours.

Part B: The average rate of change of the function represented by the table between x = 1 to x = 3 hours is 2. It means the velocity increases by 2 miles per hour.

Part C: If the velocity of the car is 60 miles/hour, then the domain is 5.

Step-by-step explanation:

Part A:

From the given table it is clear that at x=0 the value of y is 50.

It means the y-intercept of the function is 50. It represents that the initial velocity is 50 miles/hours.

Part B:

From the given table it is clear that at x=1 the value of y is 52 and at x=3 the value of y is 56. It means the graph passes through two points (1,52) and (3,56).

The average rate of change of the function is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{56-52}{3-1}=\frac{4}{2}=2$

The average rate of change of the function represented by the table between x = 1 to x = 3 hours is 2. It means the velocity increases by 2 miles per hour.

Part C:

The slope intercept of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

The slope of the function is 2 and y-intercept is 50, therefore the equation of function is

$y=2x+50$

Put y=60 in the above equation, to find the domain at velocity 60 miles/hours.

$60=2x+50$

Subtract 50 from both the sides.

$60-50=2x$

$10=2x$

Divide both sides by 2.

$\frac{10}{2}=x$

$5=x$

Therefore the domain is 5 if velocity is 60 miles/hours.