Question

hi, having trouble knowing if the equation is increasing, decreasing , constant or linear... can you help
`f( * ) = 9 * ( (1)/(7) {)}^(x)`

Answer 1

Given:

`f(x)=9((1)/(7))^x`

The equation given is an exponential function.

An exponential function is of the form,

`\begin{gathered} y=ab^x \\ \\ when\text{ }b>1,\text{ it represents an increasing function} \\ b<1,\text{ it represents a decreasing function} \end{gathered}`

Hence, for the equation;

`\begin{gathered} f(x)=9((1)/(7))^x \\ b=(1)/(7) \\ b<1 \\ Hence,\text{ the equation is decreasing} \end{gathered}`

Also, the graph is shown indicating a decreasing function.

Therefore, the answer is decreasing.