Chapter 1.2, Problem 9E

(a)

To determine

To find:The domain and range of the function $y=\frac{1}{x-2}$ .

Answer to Problem 9E

The domain and range of the function $y=\frac{1}{x-2}$ is $\left(-\infty ,2\right)\cup \left(2,\infty \right)$ and $\left(-\infty ,0\right)\cup \left(0,\infty \right)$ respectively.

Explanation of Solution

Given information:The given function is $y=\frac{1}{x-2}$ .

Calculation:

The function $y=\frac{1}{x-2}$ is defined when $x-2\ne 0$ or $x\ne 2$ . The domain of the function is the set of real numbers except the number $2$ or theinterval $\left(-\infty ,2\right)\cup \left(2,\infty \right)$ .

The function $y=\frac{1}{x-2}$ is always non zeroevery real value of $x$ . So, the range of the function is the interval $\left(-\infty ,0\right)\cup \left(0,\infty \right)$ .

Therefore, the domain and range of the function $y=\frac{1}{x-2}$ is $\left(-\infty ,2\right)\cup \left(2,\infty \right)$ and $\left(-\infty ,0\right)\cup \left(0,\infty \right)$ respectively.

(b)

To determine

To graph:The function $y=\frac{1}{x-2}$ .

Explanation of Solution

Given information:The function is $y=\frac{1}{x-2}$ .

Graph:

The graph of the function $y=\frac{1}{x-2}$ is drawn below:

  

Figure(1)

Interpretation:The graph of the function $y=\frac{1}{x-2}$ intercepts the $x-$ axis at point $\left(0,-0.5\right)$ .