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

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

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.