Question

How does the graph of
f(x)=3(4)^x-5+2/3
relate to its parent function?
I am struggling with this question and honestly don't know how to do it. Any input on the possible answers?

*Please select all correct answers*
A- The parent function has been translated to the right.

B- The parent function has been compressed.

C- The parent function has been translated up.

D- The parent function has been stretched.

Answer 1

Well let's try and establish what the parent function is here.

Answer 2

If I gave you (x-2)^2 - 3, the parent function is the parabolic function, or x^2.

That being said, what do you think the parent function of your problem is?

Answer 3

\[f(x)=3(4)^{x-5}+2/3\]

Answer 4

I don't know what a parent function is. I honestly have no clue where to start this problem, or how to approach it.

Answer 5

A parent function, as I will define it, is the most basic function by which another is based upon.

A better way to think of this is to see that the fundamental functions in algebra are all parent functions.

These are some of them.

x
x^2
x^3
sqrt(x)
abs(x)

Answer 6

So when we look at any variation of the (let's say the x function), we know that 'x' is the parent function.

Ex. 1
f(x) = x-1 relates to it's parent function 'x' by a vertical shift of -1

Ex. 2
g(x) = (x-3)^2 + 1 relates to it's parent function 'x^2' by a vertical shift of +1 and a horizontal shift of +3 (x-shifts are always opposite of the sign).

Answer 7

f(x) = x + 1
g(x) = 2x + 3
h (x) = x - 5

These are all based on the parent function: f(x) = x

Answer 8

Am I confusing you?

Answer 9

u can simply graph the function here an see the changes

Answer 10

this is graph for
\(\large\tt \begin{align} \color{black}{y=4^x}\end{align}\)

Answer 11

and this is graph for \(\large\tt \begin{align} \color{black}{y=3(4)^{x-5}+2/3}\end{align}\)

Answer 12

can u see the diffference