Question

How do the graphs of the functions f(x) = (3/2)^x and g(x) = (2/3)^x compare?

Answer 1

Answer:

Exponential function is of the form: $y =ab^x$

where a  is the initial value and b is the growth factor.

• If b> 1, then the function is exponential growth function.

• If 0<b<1, then the function is exponential decay function.

Given the parent function:

$f(x)=y = (\frac{3}{2})^x$            ....[1]

This function is an exponential growth function.

The rule of reflection over y-axis:

$(x, y) \rightarrow (-x, y)$

Apply the rule on f(x) we get;

$(\frac{3}{2})^{-x} = (\frac{2}{3})^x =g(x)$

Therefore, the function $g(x) =(\frac{2}{3})^x$ is the graph of the function f(x) reflected over y-axis.

Answer 2

The graph of the function g(x) is reflected over the y-axis to make the graph of the function f(x) and this can be determined by using the rules of transformation.

Given:

• $f(x) = \left(\dfrac{3}{2}\right)^x$

• $g(x) = \left(\dfrac{2}{3}\right)^x$

The following steps can be used in order to compare the graphs of the given function:

• Step 1 - Write the equations of the given exponential functions.

                     $f(x) = \left(\dfrac{3}{2}\right)^x$     --- (1)

                     $g(x) = \left(\dfrac{2}{3}\right)^x$     --- (2)

• Step 2 - Now, replace 'x' with '-x' in the expression (1).

                      $f(-x) = \left(\dfrac{3}{2}\right)^{-x}$

• Step 3 - Simplify the above expression.

                         $f(-x)=\left(\dfrac{2}{3}\right)^x$

                          $f(-x)=g(x)$

• Step 4 - So, from the above steps, it can be concluded that the graph of the function g(x) is reflected over the y-axis to make the graph of the function f(x).

For more information, refer to the link given below:

https://brainly.com/question/13710437