Question

i will fan and medal!!!!

Answer 1

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 2

Let's focus on part A for now

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

to find the y intercept, look at the row that has x = 0. What is the corresponding paired y value for when x = 0?

Answer 3

would it be 50

Answer 4

yes, so that's the y intercept

Answer 5

any guesses of what it means in terms of the problem?

Answer 6

the time and velocity

Answer 7

x = 0 means the time is 0 hours
y = 50 means the velocity is 50 mph

Answer 8

time = 0 hours is the lowest the time value can go, so it is the starting point or the initial time value

Answer 9

oh yea that make sense

Answer 10

this means that 50 mph is the initial velocity

Answer 11

so that would be the end to part a right

Answer 12

yes

Answer 13

ready for part B?

Answer 14

yes

Answer 15

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



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)

Answer 16

when x = 1, what is the value of y?

Answer 17

i am not sure

Answer 18

Look at the table. Locate '1' in the x column. What is right beside it?

Answer 19

52

Answer 20

yes

Answer 21

so x = 1 and y = 52 pair up
we have the ordered pair (x,y) = (1,52)

make sense?

Answer 22

yep

Answer 23

when x = 3, what is the corresponding value of y?

Answer 24

56

Answer 25

so (x,y) = (3,56) is another point

Answer 26

we have these two points
(1,52) and (3,56)

are you able to determine the slope of the line through those points?

Answer 27

would i use the equation y2-y1/x2-x1

Answer 28

yes
\[\Large m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 29

4/2

Answer 30

reduce that to get what?

Answer 31

2/1

Answer 32

which simplifies to just 2

Answer 33

so the average rate of change (from x = 1 to x = 3) is 2

this means that for each increase in the number of hours (x), the velocity (y) is increasing by 2 mph

Answer 34

this is known as the acceleration

Answer 35

so would that be the end of part 2

Answer 36

yes that wraps up part B

Answer 37

can we start part c

Answer 38

`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 39

let's look at the table again

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

Answer 40

what would be the y value for when x = 4? Any ideas?

Answer 41

hint: notice how each time x increases by 1, y will increase by 2 (hence the slope of 2/1 = 2)

Answer 42

will you explain with more depth

Answer 43

one pair is x = 0 and y = 50
another pair right underneath is x = 1 and y = 52

notice how x increases by 1 (going from x = 0 to x = 1)
at the same time, y increases by 2 (going from y = 50 to y = 52)

do you observe this pattern?

Answer 44

wait hold on.