Question

Given the exponential function f(x)=2^x, find the range when the transformation is applied: g(x)=5(2+6f(23-x)).

What would I do with the 5 in g(x)? Distributive property???

Answer 1

You're correct on that

Answer 2

How would I do it though?

Answer 3

would it be g(x) = 10 + 6f(23-x) ?

Answer 4

There are two functions. and F(x) is a function of G(x). What do you think the domain of 2^x is?

Answer 5

XER

Answer 6

Good. Now what is f(23-x)?

Answer 7

same

Answer 8

I meant what is it, not its domain? what does it mean?

Answer 9

If f(x) = 2^x

f(23-x) = ?

Answer 10

f(-(x-23))

reflection in y-axis

horizontal shift of 23 units to right

Answer 11

I was hoping you would say its

2^(23-x)

Answer 12

oh, i thought u meant what it meant as in transformations. But i get that. I just don't understand what to do with that 5 in front of g(x)

Answer 13

now we can write the function G(x)

as

G(x) = 5(2+6(2^(23-x))

Answer 14

can you see the substitution I made?

Answer 15

yes

Answer 16

now distribute the 5.

Answer 17

g(x) = 10+30(2^(23-x)

Answer 18

what about 2^(23-x)? Does that get affected?

Answer 19

Does this make more sense now? you can even distribute the 2^(23-x).

I believe it becomes 2^23-2^x

Answer 20

Oh ok so the transformed function becomes g(x) = 30(2^23-x) + 10?

Answer 21

yes

Answer 22

Ok, thank you veryyy much :D

Answer 23

your welcome =)