Question

Find the X-AND Y- INTERCEPTS OF THE FUCTION f(x)=-2|×+1|+6 enter your answers as pointx intercepts y intercepts

Answer 1

The y-intercept of a function is the value that it takes at x=0.

Evaluate f at the point x=0 to find the y-intercept:

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

Therefore, the y-intercept is 4.

The x-intercepts are the values of x that make the function to be equal to zero.

Set f(x)=0 and solve for x to find the x-intercepts:

`\begin{gathered} f(x)=0 \\ \Rightarrow-2\mleft|x+1\mright|+6=0 \\ \Rightarrow-2|x+1|=-6 \\ \Rightarrow\mleft|x+1\mright|=(-6)/(-2) \\ \Rightarrow\mleft|x+1\mright|=3 \end{gathered}`

From the expression |x+1|=3, there are two possibilities: If the expression inside the absolute value is positive, then |x+1|=x+1. If it is negative, then |x+1|=-(x+1). Consider each possibility separately:

`\begin{gathered} x+1>0 \\ \Rightarrow x+1=3 \\ \Rightarrow x=3-1 \\ \Rightarrow x=2 \\ \\ x+1<0 \\ \Rightarrow-x-1=3 \\ \Rightarrow-x=3+1 \\ \Rightarrow-x=4 \\ \Rightarrow x=-4 \end{gathered}`

There are two solutions for the equation -2|x+1|+6=0, and they are x=2 and x=-4.

Therefore, the x-intercepts are 2 and -4.