Question

Plz help!!

The table below represents the distance of a train from its destination as a function of time:
Time (hours) x       Distance (miles) y
0                            665
1                             570
2                            475
3                            380
4                            285
Part A: What is the y-intercept of the function, and what does this tell you about the train?
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 4 hours, and tell what the average rate represents.
Part C: What would be the domain of the function if the train continued to travel at this rate until it reached its destination?

Answer 1

Part A: The y-intercept is 665. It is starting at 0 on the x axis. The train starts 665 miles from it's destination, so the intercept is 665.

Part B: As x increases by 1, y decreases by 95. This slope can be shown as -95/1. The rate is 95 miles per hour, since the train covers 95 miles for every hour it travels.

Part C: The train would take 7 hours at the present rate to reach it's destination.

Answer 2

y-intercept states that the graphs cuts the y-axis.

i.e, (0, y)

As per the statement:

The given table represents the distance of a train from its destination as a function of time;

here, x represents the time in hours and y represents the Distance in miles

Part A.

To find the y-intercept of the function.

by definition:

at x = 0 hours

⇒y = 665 miles

or

y(0) = 665 miles

⇒Y-intercept = 665 miles and It means that the train starts 665 miles from it's destination.

Part B

To find the average rate of change of the function represented by the table between x = 1 to x = 4 hours

Formula for average rate of change(A(x)) of y=f(x) over interval [a, b] is given by:

`A(x)=(f(b)-f(a))/(b-a)` ....[1]

At x = 1

y =f(1) = 570

At x = 4

then;

y = f(4) = 285

Substitute the given values in [1] we have;

`A(x)=(f(4)-f(1))/(4-1)`

⇒
`A(x)=(285-570)/(3)=(-285)/(3)`

⇒
`A(x) = -95`

As x increases by 1, y decreases by 95. This slope = -95

⇒The rate is 95 miles per hour, since the train covers 95 miles for every hour it travel.

Part C.

Using slope intercept form:

Equation of line is given by:

y = mx+b ; where, m is the slope or rate and b is the y-intercept

From above Part A and B:

m = -95 and b = 665

then;

y = -95x+665 ....[2]

We have to find the the domain of the function if the train continued to travel at this rate until it reached its destination

Substitute y = 0 in [2] and solve for x:

0= -95x+665

Add 95x to both sides we have;

95x = 665

Divide both sides by 95 we have;

x = 7 hours

Therefore, the domain of the function if the train continued to travel at this rate until it reached its destination would be 7 hours