Chapter 4.3, Problem 54E

To determine

To find: The graph for the function and the find he domain, range, and asymptote.

Answer to Problem 54E

The required graph is shown in Figure 2, the domain of the function is $\left(0,\infty \right)$ and its range is $ℝ\text{or}\left(-\infty ,\infty \right)$ . The vertical asymptote of the graph is $x=0$ .

Explanation of Solution

Given:

The given function is $f\left(x\right)=-{\log }_{10}x$ .

Calculation:

Consider the parent function is,

  $f\left(x\right)={\log }_{10}\left(x\right)$

The graph for the equation $f\left(x\right)={\log }_{10}\left(x\right)$ is shown in Figure 1

Figure 1

The graph for the function $f\left(x\right)=-{\log }_{10}x$ is obtained by reflecting the graph $f\left(x\right)=-{\log }_{10}x$ to the x axis.

The domain set of the x values is the set of functional values.

From the domain of the graph is,

  $\left(0,\infty \right)$

From the graph the range of the graph is,

  $\left(-\infty ,-\infty \right)$

The vertical asymptote of the graph is y axis that is the vertical asymptote of the graph is $x=0$ .