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.

Question

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Respuesta :

jalycia27 jalycia27 · Answer 1 · 2019-04-14T21:08:00+02:00

Answer:

A,C,&D

Step-by-step explanation:

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lublana lublana · Answer 2 · 2019-12-19T06:24:54+01:00

Answer:

A,C and D

Step-by-step explanation:

We are given that

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

We have to find the graph of given function relate to its parent function.

Let parent function

[tex]g(x)=4^x[/tex]

Now, the graph shift 5 unit towards right by the rule of transformation

[tex]g(x)\rightarrow g(x-5)[/tex]

Therefore, by using this rule then, we get

[tex]g(x)=(4)^{x-5}[/tex]

Now, stretch vertically 3 times the previous graph by using the rule of transformation

[tex]f(x)\rightarrow 3f(x)[/tex]

Now, after applying this rule we get

[tex]g(x)=3(4)^{x-5 }[/tex]

Now, shift the graph [tex]\frac{2}{3}[/tex] unit upward by the rule of transformation

[tex]f(x)\rightarrow f(x)+\frac{2}{3}[/tex]

After applying this rule then, we get

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

Hence, options A ,C and D are true.