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

Time (hour) x Velocity (miles/hours) y
0 50
1 52
2 54
3 56

Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points)

Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points)

Part C: What would be the domain of the function if the velocity of the car was measured until it reached 60 miles/hour and the car does not change motion? (2 points)

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

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{56-52}{3-1}=\frac{4}{2}=2[/tex]

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

[tex]y=mx+b[/tex]

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

[tex]y=2x+50[/tex]

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

[tex]60=2x+50[/tex]

Subtract 50 from both the sides.

[tex]60-50=2x[/tex]

[tex]10=2x[/tex]

Divide both sides by 2.

[tex]\frac{10}{2}=x[/tex]

[tex]5=x[/tex]

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