Question

g(x)=x^2+1 shifted two units to right

Answer 1

Are you supposed to graph it, write the equation, what?

Answer 2

write the equation

Answer 3

To shift to the right, just replace x with x-2.

Answer 4

x-2^2+1 ?

Answer 5

g(x) = (x-2)^2 + 1

Answer 6

No, you have to square the whole (x-2)

Answer 7

simplified, it's x^2-4x+5

Answer 8

okay thank you

Answer 9

welcome

Answer 10

to move to the left, would it be (x+2)^2+1

Answer 11

?

Answer 12

Yes. In general, to move right or left, you subtract or add from the argument to the function. Take y = x^2: at x = 0, y = 0^0 = 0. If you subtract 1 from x before squaring it, that means that the spot where y = 0 is moved by 1 unit along the x axis, and x = 1 is where the feature that happened at x=0 previously now occurs. Does that make sense?

Answer 13

yes! that actually makes alot of sense. this isnt related, but could you explain to me how to tell if a graph is a function ?

Answer 14

Yes, I can :-) If there is any spot on the graph where you can draw a vertical line and cross the curve twice, it is not a function. A function is defined as only having 1 value of y for any given value of x.

Answer 15

so a parabola would be a function ?

Answer 16

If it is a parabola of the sort that opens up or down, yes. One that opens right or left, no.

y=x^2 is a function, x = y^2 is not.

Answer 17

okay, that makes sense. thank you for explaining to me

Answer 18

The inverse of a function is the function reflected about the line y = x, so an inverse of a function is not a function.

Answer 19

That last statement is not true. If it were, there would be no one-to-one functions.

Answer 20

give me an example of what you mean.

Answer 21

sorry, you're right, my statement is overly broad there.

Answer 22

Example: y=2x is a function (y is a function of x), so is the inverse x=y/2 (x is a function of y); or, if you prefer, reversing the variable mapping, y=x/2 (y is a function of x); either way.

Answer 23

np, good thoughts nonetheless

Answer 24

no inverse of a function where a horizontal line crosses the graph with multiple intersections...

Answer 25

(essentially the inverse of the vertical line test)

Answer 26

the inverse of a function where a horizontal line crosses the graph with multiple intersections is not a function...that's what I mean to say :-)

Answer 27

i have another question, im sorry !

Answer 28

answering your questions is why I'm here!

Answer 29

g(x)=x^3 stretched to be twice as tall, im confused because its a cubic function

Answer 30

Okay, I meant to touch on this too when we were talking about shifting right and left. If you want to shift up and down, you add or subtract to the result of the function. Agreed?

Answer 31

yes!

Answer 32

It's like printing the function on a transparency and sliding it up and down the y-axis.

Answer 33

what does stretch mean ?

Answer 34

now, stretching (or compressing) along the y-axis is similar to printing on transparent rubber...think of what happens to a balloon with printing on it when you blow it up.

Answer 35

what would be the mathematical operation to do that, do you think?

Answer 36

hmm ... muliplication. the print would get bigger

Answer 37

yes!

Answer 38

am i wrong ?/:

Answer 39

aww yay

Answer 40

and multiplication by a fraction would make it smaller.

Answer 41

Now, here's a trickier one: how do you stretch or compress along the x-axis?

Answer 42

uhhh .... divide ? assuming

Answer 43

well, maybe. The subtle point here is that like we did to shift right and left, we change the argument to the function, instead of the result of the function...

Answer 44

Think about that for a minute...

Answer 45

okay, time's up! :-)

Answer 46

wait - so x^3 stretched twice it's height would be, x^3(2)

Answer 47

Say we have a sine wave...y = sin x:



Now, if we change that to be y = sin 2x, the curve wiggles twice as many times in a given amount of x-axis, right?