Question

On a coordinate plane, a red line, labeled g of x, begins on a negative slope, crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and crosses the x-axis on a positive slope at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 2) and the x-axis at (2, 0).
Which statement is true regarding the functions on the graph?

f(2) = g(2)
f(0) = g(0)
f(2) = g(0)

Answer 1

f(2) = g(2) is true.

Reason: f(x) is the line through (0,2) and (2,0), so f(x) = -x+2 ⇒ f(2)=0. g(x) is the V-shaped graph with vertex (0,-2) and zeros at x=±2, so g(2)=0. Thus f(2)=g(2)=0. The other equalities are false (f(0)=2 while g(0)=-2).