Question

The graph of f(x) = |x| − 2 has an x-intercept at ???

A- (0,0)
B- (0,-2)
C- (-2,0)
D- (2,2)

Answer 1

The correct answer is option C: (-2, 0).

To solve for the x-intercepts of a function, f(x) (or y) must equal 0. When f(x) (or y) = 0, there is no vertical change, and so the corresponding x-coordinate will lie directly on the x-axis, intercepting it.

So, let’s set f(x)=0 and solve for x:

(0)=|x|-2

Add 2 to both sides:

2=|x|; |x|=2

x=-2, 2

Thus, the x-intercepts are at the points:

(-2, 0) and (2, 0).

(-2, 0) is an answer in the choices, so it is the only correct one out of the others.