Question

Give the equation of the function g whose graph is described.

The graph of f(x) = |x| is vertically stretched by a factor of 4.5. This graph is then reflected across the x-axis. Finally, the graph is shifted 0.47 units downward.

Answer 1

Sup sup sup!

Answer 2

haha hey just the usual

Answer 3

that's good...alrighty lets take a look at this.

Answer 4

alright

Answer 5

Ah so it's a transformation problem, do you know how to start this?

Answer 6

verrtically stretched so on the y axis, and then it's reflection makes it -4.5 then the shift dow is -.47

Answer 7

yup we need to take it one step at a time, so how do we stretch ƒ(x) = |x| by 4.5 vertically?

Answer 8

f(x) is what the ????? are

Answer 9

y?

Answer 10

a vertical stretch is a stretch away from the x

Answer 11

well no. a vertical stretch is just a vertical stretch as if the graph you are graphic on was made of clay and you streched while the function was written on it

Answer 12

oh ok then, right

Answer 13

so do you know how stretch something vertically on a graph using mathematical manipulations?

Answer 14

no i dont think i do

Answer 15

that's fine! Let's learn about it now! So to vertical manipulate an equation all we need to do it multiple whatever y's equal to by a value. So for example:\[y = x\] to stretch that by 10 times we do this:\[y=10 \times x\]Do you have a graphing calculator? If so plot these two equations.

Answer 16

yeah i do

Answer 17

so do you see how y=x looks like it was stretched by a factor of 10?

Answer 18

i graphed them

Answer 19

yes

Answer 20

nice so now you know how to stretch and shrink things vertically! right?

Answer 21

right

Answer 22

ok so question do you want to know further manipulations or just the ones in the problem?

Answer 23

ok one more then problem

Answer 24

ok hmmm let's go with horizontal streching

Answer 25

to horizontally stretch a function all we need to do is mulitply x with a value but a bigger number compresses it while a smaller number stretches it: so instead of thing that the y=x was vertically stretched you could have thought of it as being compressed horizontally, does this make sense?

Answer 26

umm kinda
o instead of thing that the y=x was vertically stretched you could have thought of it as being compressed horizontally, does this make sense? this part ????

Answer 27

you don't get that part?

Answer 28

no not that part

Answer 29

haha ok let's see, if I can put it another way. so you graphed y = x and y = 10x right?

Answer 30

yeah

Answer 31

Vertical stretching implies the graph is getting pulled away from the x-axis.
When you pull something away from the x-axis you are making it closer to the y-axis which implies horizontal compression.

Answer 32

exactly what aum said does that make sense?

Answer 33

yes it does

Answer 34

nice cool alright so lets move on to the next part of the problem: the graph is reflected across the x-axis.

To do this you simply need to multiply y by -1 so if:
\[y = (x-3)\] and you want to reflect this across the x axis we simply do this:
\[y = -1 \times (x-3)\]
does that make sense?

Answer 35

yes

Answer 36

alrighty the last part says that it was shifted downward which if I remember correctly you know how to do?

Answer 37

I just realized that you said that whole thing...sorry I was helping another person...do you have an answer to this problem actually?

Answer 38

its ok i was reading it

Answer 39

wait so do you know how to manipulate the equation?

Answer 40

haha and you would be dead on correct!

Answer 41

oh yes!

Answer 42

next one?

Answer 43

yup the next one!

Answer 44

do you know how to do this?

Answer 45

i graphed it and wherever it crosses y?

Answer 46

well no a vertical asymptote is when function head off to infinity (either negative or positive) in the middle of the function. And there's a way to tell from just the equation itself!

Answer 47

want to know how?

Answer 48

yes of course

Answer 49

haah ok here it is whenever the function attempts to divide by 0, is where a vertical asymptote can lie.

Answer 50

does that make sense?

Answer 51

9 and -8?

Answer 52

yup!! Correct! now there's a reason as to why I said can instead of will, want to know why?

Answer 53

no need to ask, of course

Answer 54

haha because imagine if in this problem alongside (x-5) we had a (x+8) so the function would be: \[\frac{(x-5)(x+8)}{(x-9)(x+8)}\] there actually wouldn't be a asymptote at x =-8 but rather there would be something called a hole. Do you know what a hole is?

Answer 55

ummm a parabola on both sides of x intercept?

Answer 56

umm no... did you graph this function?

Answer 57

or rather graph this function and the problem's if you haven't already

Answer 58

give me a sec