Question

The red graph (1) is the graph of f(x) = 2x. Describe the transformation of the blue function (2) and write the equation of the graph.

Answer 1

@nphuongsun93

Answer 2

you understand it @Romero orrr..?

Answer 3

To clarify, that is \(f(x)=2^x\).

Answer 4

yes

Answer 5

Looks like it was shifted to the right 5 and up 2, right?

Answer 6

i believe so?

Answer 7

Okay, so if we're shifting a graph up 2, how would you change the equation to represent that? Think about it this way: we're making it so that for every value of x, the value of y is 2 more than it was in the old equation.

Answer 8

add +2 i guess?

Answer 9

Right, so how would you write that equation? The whole equation, I mean.

Answer 10

fx=2x+2?

Answer 11

Right. Just to be clear, it's better to write it as 2^x, so that we know it's \(2^x\) rather than just \(2x\).

Anyways, next step, you want to shift it to the right five. So what that means is for each x, we want the value of y to be what it used to be five to the left. Does that make sense why that is?

Answer 12

so is that the final equation?

Answer 13

We still have to shift it five to the right, remember?

Answer 14

so +5?

Answer 15

That would shift it five up, not five to the right :P

Answer 16

k..

Answer 17

To shift an equation to the right or left, it's a bit more complicated. We basically want to change which value of x we're looking at, so we have to change it in the actual exponent. The part that's counterintuitive is that to shift to the left we add, and to shift to the right we subtract. So, for example, if we wanted to shift \(f(x)=2^x\) to the right one, we would do \(f(x)=2^{x-1}\).

Answer 18

ok...is that the final equation

Answer 19

f(x)=2^x+5

Answer 20

whats the transformation of the blue function?

Answer 21

Remember to use parentheses to make clear what you're saying. For example, if you want to say \(f(x)=2^{x+5}\), say 2^(x+5), but if you want to say \(f(x)=2^x+5\) then just say 2^x+5.

So, the way you said that, I would interpret as \(f(x)=2^x+5\), which is the original graph shifted up 5. Remember, we want to shift it up 2, and to the right 5.

Answer 22

can you show me

Answer 23

Okay, here's another example. If we wanted to shift it down 3 and to the left 4, we would do this: \(f(x)=2^{x+4}-3\). The +4 in the exponent shifts it to the left 4, and the -3 shifts it down 3.

Answer 24

f(x)=2^x+5+2

Answer 25

First, remember to use parentheses so that it is clear what you mean. Second, remember that when shifting left and right, you add to shift left, and subtract to shift right.

Answer 26

ok..how does that look?!

Answer 27

How does what look? For an example of using parentheses, the example that I just gave where I shifted it down 3 and to the left 4 could be written as f(x)=2^(x+4)-3.

Answer 28

the final equation. How does the final equation look??

Answer 29

Why do you need to ask me? You have all the tools you need to put it together. I've told you how it works, and given you multiple examples. What do you think the final equation is?

Answer 30

I. DONT.KNOW.

Answer 31

You don't need to know, you just need to think. Try to figure it out. Actually work on it. I'll tell you if what you come up with is correct or not.

Answer 32

f(x)=2^(x+5)+2

Answer 33

That's very close. That actually shifts it to the left instead of to the right, though. When shifting left and right, you use + to shift left, and - to shift right.

Answer 34

soooooooooo -2?

Answer 35

?

Answer 36

whats the transformation of the blue function?

Answer 37

The +2 is to shift it up. The part that is wrong is the left/right shift, that's the one that needs to be - instead of +.

Answer 38

x-5+2?

Answer 39

Write the whole thing properly so I know what you mean

Answer 40

f(x)=2^(x-5)+2

Answer 41

???????????????

Answer 42

can anyone help me? ive been stuck on this problem for 3 hours..literally. I really just need the answer

Answer 43

Yeah, the last thing that you posted was correct.