Question

Given its parent function, f(x) = 2x, what is the equation of the function shown?

Answer 1

wow cool picture c:

Hmm I'm not quite sure what the question is asking.
Oh a graph, good.

Answer 2

haha thanks i think

Answer 3

Hmm I'm not really sure what the parent function thing is about...

But it appears we have an exponential function graphed.
Oh oh oh I see, you meant to write \(\large f(x)=2^x\)

Ok ok ok now it makes sense.
That is our parent function, and we have some alterations applied to it.

Answer 4

hhahah heheh

Answer 5

Normally, \(\large 2^x\) would have an `asymptote` at y=0.
See the red dotted line? Not the one on your cheek, the one on the graph.

Our asymptote appears to have been moved to y=2.
So the function has been shifted `up` two units.
We can write it like this,\[\large f(x)=2^x+2\]

Ok let's see if there is anything else going on. :o hmm

Answer 6

If it was \(\large f(x)=2^x+2\), then it would pass through the point \(\large (0,\;3)\).

But it doesn't. It's passing through \(\large (0,\;5)\).
So we have some scalar being applied to it.

\[\large f(x)=a2^x+2\]

We can plug in our coordinate pair to solve for the missing value a.

\[\large (0,\;5) \qquad \rightarrow \qquad 5=a \cdot 2^0+2\]

What do you get for \(\large a\)? c:

Answer 7

2x+5?

Answer 8

It should be just a number c: We plugged in a value for our x, so there isn't an X when we're solving for a.

Answer 9

What is \(\large 2^0=\)

Answer 10

i got h(x) = 2^x +5 or 3(2)^x + 2 or 5(2)^x + 3 or 7(2)^x + 2

Answer 11

0

Answer 12

\(\large 2^0=1\)
If you're unsure about that, throw it into your calculator c:
So that gives us,\[\large 5=a +2\]Now solve for \(\large a\) ! :D

Answer 13

3

Answer 14

Yay gj, now plug that a value into the function we were working on.

\(\large f(x)=a2^x+2\)
And you should have your answer.

Answer 15

If this was confusing, there is another way to do it setting up a system of equations. But whatev :D

Answer 16

so 3(2)^x + 2?

Answer 17

yes

Answer 18

thank yewwwwwwww!!!