Question

Find the x- and y-intercepts of the graph of the function f(x)=−2|x−1|+6. Enter your answers as points, (a,b). Enter the x-intercepts in order of increasing x-value. If there are no x-intercepts, enter NA in both answer areas. x-intercepts: y-intercept:

Answer 1

To find the y-intercept, set x=0 and find the value of the function:

`f(x)=-2|x-1|+6`
`\begin{gathered} \Rightarrow f(0)=-2|0-1|+6 \\ =-2(1)+6 \\ =-2+6 \\ =4 \end{gathered}`

Then, the y-intercept is (0,4).

To find the x-intercept, set f(x)=0 and solve for x:

`\begin{gathered} f(x)=0 \\ \Rightarrow-2|x-1|+6=0 \\ \Rightarrow2|x-1|=6 \\ \Rightarrow|x-1|=(6)/(2) \\ \Rightarrow|x-1|=3 \\ \Rightarrow x-1=\pm3 \\ \Rightarrow x=1\pm3 \\ \Rightarrow x_1=4;x_2=-2 \end{gathered}`

Therefore, the x-intercepts are (4,0) and (-2,0).