Question

The table below represents the distance of a car from its destination as a function of time:


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, and tell what the average rate represents. (4 points)

Part C: What would be the domain of this function if the car traveled the same rate until it reached its destination? (2 points)

Answer 1

The y-intercept is what 'x' is when y = 0.

Answer 2

So what's the y-intercept?

Answer 3

y represent the distance with miles , this tell

Answer 4

Look at the table..what number is next to the 0? @Kidthatbro8

Answer 5

900 is next to 0.

Answer 6

the car is walking in speed , you give how many hours the function give you the number of miles

Answer 7

Yep, so that's our y-intercept.

This means that the distance away from the destination was 900 miles.

Answer 8

That takes care of Part A.

Now for Part B..

To calculate the average rate of change, we use the slope formula.

When x = 1, y = 850
When x = 3, y = 750

Now plug them into the slope formula:

\(m = \dfrac{750-850}{3-1}\)

Can you simplify that?

Answer 9

-100 / 2 ?

Answer 10

No, check again..2 is right, but -100 is not.

Answer 11

m = -50 and the slope represent the speed of this car,
the speed is -50 miles/hours

Answer 12

i'm not sure how i would check it, could you help ?

Answer 13

Oh wait -100 is correct..my bad.

Answer 14

Now divide -100 / 2.

Answer 15

oh, okay. -50, right ?

Answer 16

Yep, so the average rate of change from x = 1 to x = 3 is -50.

Answer 17

This represents the average distance away from the destination between hours 1 and 3.

Answer 18

the speed may be negative .... this said the car is walking opposite of positive axis

Answer 19

That takes care of Part B.

Now for Part C:

The domain would be the x-value..so it's basically asking how many hours it will take to reach its destination.

Answer 20

f(x) =0 this mean that car is reach the goal .
f(x) = -50x +900;
0 = -50x+900
900 =50x
x= 18

Answer 21

it's need 18 hours to reach the goal

Answer 22

If you look at the table you can see that after each hour passes 50 miles are taken off.

So we can write the equation:

y = 900 - 50x

Now we plug in 0 for y:

0 = 900 - 50x

Now we subtract 900 to both sides:

-900 = -50x

Now can you divide -900 / -50? @Kidthatbro8

Answer 23

18.

Answer 24

Yep, so it takes 18 hours to reach his destination..so the domain will be 0-18.

Answer 25

And that's your whole question :)

Answer 26

oh, thank you so much !

Answer 27

No problem.