Question

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

$\mathrm{f}\left(\mathrm{x}\right)=\frac{2}{3}\mathrm{x}-2.$

Short answer

Domain of linear function is$(-\infty ,\infty ).$Range of linear function is$(-\infty ,\infty ).$

Step-by-step solution

Step 1. Given Information

Given that the linear function equation is$\mathrm{f}\left(\mathrm{x}\right)=\frac{2}{3}\mathrm{x}-2.$

Step 2. Linear function

It is confirm that the given linear function is in slope-intercept form.

Slope is $\mathrm{m}=\frac{2}{3}.$The y-intercept can be found as $(0,-2).$Graph can be drawn using slope and intercept are drawn as,

Step 3. Domain and range

Because given function is a linear function, domain of linear function is all real numbers. Domain for the given linear functions is $(-\infty ,\infty ).$

Because given function is a linear function, range of linear function is all real numbers. Range of the linear function is $(-\infty ,\infty ).$