Question

Please help! Use the graph of f to describe the transformation that yields to the graph of g.

1) f(x)=log10(x), g(x)=log10(x+7)

2) f(x)=log2(x), g(x)=3+log2(x)

Answer 1

Ok, when you have f(x)=2x to shift it a units left you add a inside the parenthesis. Like this, f(x)=2(x+a)

Answer 2

Another way of expressing what SZ has just shared with us follows:

Given the graph of f(x) = 2x, shifting the graph "a" units to the left results in the new function g(x) = 2(x-[-a]). Shifting the same original graph "a" units to the right results in the new function h(x) = 2(x-a). Summary: to the left: [-a]; to the right: [a].

Answer 3

where is the 2x coming from? I don't understand :(

Answer 4

it's an example.

Answer 5

oh I see! sorry

Answer 6

Please go back to the first problem, which does involve shifting of the graph of the original function horizontally. How far is the graph shifted, and in which direction?

Ali, SZ made up this example to make his point, and is correct as far as he goes.

Answer 7

so then in this case #1 would shift to the left 7 times?

Answer 8

does that mean that #2 would only go down 3 units since it is just +3?

Answer 9

Yes, Ali, except it's 7 units to the left (not 7 times). :)

Answer 10

haha thank you!! :) can you help me understand #2 better though? that one is trickier for me because of the way it is set up :o

Answer 11

Ali: Please re-think your most recent response, the one involving vertical shifting.

Answer 12

+3 (outside the parenthesis) like f(x)=x to f(x) = x +3 would be 3 units up I think, NO?

Answer 13

\[g(x)=3+\log2(x)\]

Answer 14

its supposed to be a little 2 if that makes a difference :o

Answer 15

Yes, SZ. the graph of g(x) = x + 3 is identical to the graph of f(x) = x, except that the whole graph of f(x) = x is shifted upward by 3 units.

Answer 16

K

Answer 17

Ali: what are the instructions for this most recent problem (involving the log to the base 2 of x)?

Answer 18

why is it shifting upward? doesn't it go down since the 3 is positive?

Answer 19

it says "Use the graph of f to describe the transformation that yields the graph of g"

Answer 20

and then this problem that I need help with is:

f(x)=log2(x) , g(x)=3+log2(x)

Answer 21

Ali: I see you're trying to apply the principle used with horizontal shifting to vertical shifting. But the rule's different in this particular problem. If y = f(x) + a, we shift the graph up; if y= f(x) - a, we shift the graph down, both by "a" units.

Answer 22

f(x)=log2(x) , g(x)=3+log2(x) same as
f(x)=log2(x) , g(x)=log2(x)+3

Answer 23

ohh that makes sense

Answer 24

I hate to back off in midstream, but must log off my computer now. I'd suggest you re-post your second question as a new problem. SZ is indeed making a lot of sense here.

Answer 25

i see! so would it be that it goes up 3 units and thats it or does the graph do anything else?

Answer 26

thanks so much y'all!

Answer 27

mathmale ? virus scanning?

Answer 28

I recently detected a huge virus, " GorillaPrice" or something like that, it said that it was antivirus, but my comp detected it.

Answer 29

Are you clear, or need more help?

Answer 30

aw man thats no fun to deal with!

Answer 31

can you just clarify really quick, for the second problem the graph shift up 3 units and thats all?

Answer 32

or does it move anywhere else?

Answer 33

If you mean

f(x)=log2(x) , g(x)=3+log2(x)

then yes, only shifts up 3.

Answer 34

yes, thank you so much i really appreciate it! :)

Answer 35

I haven't really helped, but glad you understand this, good luck!

Answer 36

thanks :D

Answer 37

YW