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

Sample Response: The graphs are reflections of each other over the y-axis. The graph of g(x) shoes exponential decay, while the graph of f(x) shows exponential growth.