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.

Answer 1

Given the function:

`fx=-2|x-1|+6`

Let's find the x-intercepts and the y-intercepts of the graph.

• x-intercepts:

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

`\begin{gathered} 0=-2|x-1|+6 \\ \end{gathered}`

Subtract 6 from both sides:

`\begin{gathered} 0-6=-2|x-1| \\ \\ -6=-2|x-1| \end{gathered}`

Divide both sides by -2:

`\begin{gathered} (-6)/(-2)=(-2|x-1|)/(-1) \\ \\ 3=|x-1| \\ \\ x=\pm3+1 \\ \\ x=3+1,-3+1 \\ \\ x=-2,\text{ 4} \end{gathered}`

Therefore, the x-intercepts are:

x = -2, 4

• y-intercept:

To find the y-intercept, set the value of x to zero and solve for f(x).

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

Yes, therefore, the y-intercept is:

y = 4

ANSWER:

• x-intercepts: x = -2, 4

,

• y-intercept: y = 4