Question

How does the graph of f(x) = 3(4)*t + relate to its parent function?A. The parent function has been translated to the right.B. The parent function has been compressed.C. The parent function has been stretched.D. The parent function has been translated up..

Answer 1

As per given by the question,

There are given that the function,

$f(x)=3(4)^{x-5}+\frac{2}{3}$

Now,

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

Then,

Let parent function is;

$g(x)=4^x$

According to the question,

The graph shift 5 unit towards right, because there are given that,

$g(x)=g(x-5)$

Now,

Stretch vertically 3 times by using the rule of transformation.

That means, there are already given tha;

$f(x)=3(4)^{x-5}$

Now,

Again, according to the question,

Shift the graph 2/3 unit upward, because there are also mentioned ,

$f(x)=f(x)+\frac{2}{3}$

So,

With the help of these three transformation rule, we can find the option.

Hence, the option A, C, and D is correct.