Question

a) Graph each function. b) State its domain and range. Write the domain and range in interval notation.

$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{2}\mathrm{x}+1$

Short answer

The domain of the linear function is$(-\infty ,\infty )$. The range of the linear function is$(-\infty ,\infty ).$

Step-by-step solution

Step 1. Given Information.

a) Graph the function,

$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{2}\mathrm{x}+1$

Step 2. Linear Function

It is in the form of slope-intercept concept and the slope is $\mathrm{m}=\frac{1}{2}.$The y-intercept is$(0,1).$ The graph can be drawn as,

Step 3. Domain and range

Given function is a linear function, domain of linear function is all real numbers.

Domain of the linear functions is$(-\infty ,\infty ).$Given function is a linear function, range of linear function is all real numbers. Range of the linear function is $(-\infty ,\infty ).$