Question

Write the rule of a function g whose graph can be obtained from the graph of the function f(x) = x2 - x + 3 by reflecting the graph in the x-axis, then shifting it vertically upward 5 units.

Answer 1

g(x)= ???

Answer 2

hehe im super rusty on these but can work you through it if oyu would like

Answer 3

yes i would like lol

Answer 4

ok so whats the grah look like?

Answer 5

is it a line?

Answer 6

a circle?

Answer 7

no graph

Answer 8

thats the only info they give me

Answer 9

yes that is a function and has a graph

Answer 10

its a parabola i think?

Answer 11

yep!

Answer 12

does it open up or down?

Answer 13

we're doing transformations

Answer 14

exactly we are trnsforming the graph

Answer 15

up

Answer 16

what would we do to it to reflect it on the x axis?

Answer 17

we always want the function to be negative...

Answer 18

so... shift to the right?

Answer 19

well lets first reflect it then well pellet it

Answer 20

ok proceed lol

Answer 21

you there?

Answer 22

I think it's g(x) = -x^2 + x + 2, but don't quote me

Answer 23

my guess would be -x^2 + x + 8

-Hero heres my logic.. we want our y values to be 5 greater than what we got before so would we add 5 to the right side?

Answer 24

Hero, you are correct. Tell me how you got your answer.

Answer 25

Yes, I know I am correct

Answer 26

ohh i seehehe gotta flip the whole thing

Answer 27

Yup

Answer 28

Please explain and draw out if you want as well

Answer 29

hero want me to explain it?

Answer 30

Go ahead

Answer 31

ok so mario our original equation is

x^2 - x + 3 = y

we want to make all the +y valuse negitive so that it looks like the pic i drew above

x^2 - x + 3 = -y

that will flip it upside down

Answer 32

What the...? C'mon man, you're confusing him

Answer 33

multiply each side by -1

-x^2 +x -3 = y

Answer 34

next we want to add 5 so that our y values are 5 greater

Answer 35

-x^2 + x -3 +5 = y

Answer 36

then...

Answer 37

simplify..

thats my thought process anyways.. when i took this course i simply memorized what each transformation required.. it helps in the long run to tho to understand the graph and what must be done to it to change it

Answer 38

There is something wrong with your steps and your approach

Answer 39

whats that?

Answer 40

Hero how did u do it?

Answer 41

hehe it works in my mind lol us engineers think weird sometimes..

mario look in your book at the section that has transformations in it.. they describe it much better than i or hero

Answer 42

I haven't even begun to describe it yet. I was allowing you to do it, but it didn't turn out so well.

Answer 43

well begin then lol

Answer 44

i got to go but when i come back tomorrow there better be an explanation lol

Answer 45

Okay, so we have f(x) = x2 - x + 3

and we were asked to flip f(x) over the x axis, and then, shift it up vertically by 5.

In other words, change f(x) to -f(x) + 5

Now, if we flip f(x) over the x axis, we will have -f(x), meaning the opposite of f(x).

This simply means that all of the signs of f(x) will change.

So -f(x) becomes -x^2 + x - 3

And then -f(x) + 5 becomes -x^2 + x + 2

Which is the correct answer.

Answer 46

Ok that makes sense. Thanks.