Question

1. Graph & give the domain, range, &
zeros of y=f(x) = 3x - 6

Answer 1

The given function is

`f(x)=3x-6`

The domain is all the values of x that make the function defined

Since all real numbers make f(x) defined, then

The domain is all real numbers

`D=(-\infty,\infty)`

The range is all values of y corresponding to the domain

The range also is all real numbers

`R=(-\infty,\infty)`

To find the zeroes equate f(x) by 0

`\begin{gathered} f(x)=0 \\ \\ 3x-6=0 \end{gathered}`

Add 6 to both sides

`\begin{gathered} 3x-6+6=0+6 \\ \\ 3x=6 \end{gathered}`

Divide both sides by 3

`\begin{gathered} (3x)/(3)=(6)/(3) \\ \\ x=2 \end{gathered}`

The zero of the function is (2, 0)

To draw the graph we will use 2 points

(2, 0) x-intercept

(0,-6) y-intercept

The red line is the graph of the given function