Question

Identify the x and Y intercepts of the graph of the function.

Answer 1

we have the function

$f(x)=-3\lvert x-2\rvert-1$

Remember that

y-intercept (is the value of the function f(x) when the value of x=0)

so

For x=0

substitute in the given function

$\begin{gathered} f(x)=-3\lvert0-2\rvert-1 \\ f(x)=-3\lvert-2\rvert-1 \\ f(x)=-3(2)-1 \\ f(x)=-7 \end{gathered}$

so

the y-intercept is the point (0,-7)

Part 2

x-intercept (is the value of x when the value of the function f(x)=0

so

For f(x)=0

substitute

$\begin{gathered} -3\lvert x-2\rvert-1=0 \\ -3\lvert x-2\rvert=1 \\ \lvert x-2\rvert=-\frac{1}{3} \end{gathered}$

this equation has no solution (the absolute value of any number cannot be a negative number)

that means

the given function has no x-intercepts