Chapter 3, Problem 5CR

To determine

To identify: Graph the exponential function by hand and identify any asymptotes and intercepts and determine whether the graph of the function is increasing or decreasing.

Answer to Problem 5CR

The asymptote and the intercept is $y=0$ and $\left(0,1\right)$ respectively. And the function is decreasing on $\left(-\infty ,\infty \right)$ .

Explanation of Solution

Given information:

The given exponential function is $f\left(x\right)=8^{-x}$ .

Calculation:

For the function $f\left(x\right)=a^{-x}$ .

The asymptote is x-axis as horizontal asymptotes. The intercept is $\left(0,1\right)$ . And the graph is decreasing when $a>0$ and increasing when $0<a<1$ .

Therefore,

For the function $f\left(x\right)=8^{-x}$ .

The asymptotes is $y=0$ .

The intercept is $\left(0,1\right)$ .

And since $8>1$ . Thus, the function is decreasing on $\left(-\infty ,\infty \right)$ .

The graph of the function is drawn below:

  

Hence,

The asymptote and the intercept is $y=0$ and $\left(0,1\right)$ respectively. And the function is decreasing on $\left(-\infty ,\infty \right)$ .