Question

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)

Answer 1

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.

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=(y_2-y_1)/(x_2-x_1)=(56-52)/(3-1)=(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.

`(10)/(2)=x`

`5=x`

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