Question

Which statement is true regarding the graphed functions?

On a coordinate plane, a straight red line with a positive slope, labeled g of x, crosses the x-axis at (negative 6, 0) and the y-axis at (0, 6). A straight blue line with a negative slope, labeled f of x, crosses the x-axis at (negative 0.75, 0) and the y-axis at (0, negative 2).

f(4) = g(4)
f(4) = g(–2)
f(2) = g(–2)
f(–2) = g(–2)

Answer 1

First write the equations.

g passes through (−6,0) and (0,6) so g(x) = x + 6.
f passes through (−3/4,0) and (0,−2) so f(x) = (−8/3)x − 2.

Evaluate:
- g(4) = 4 + 6 = 10, f(4) = (−8/3)*4 − 2 = −38/3 (not equal).
- g(−2) = −2 + 6 = 4, f(−2) = (−8/3)*(−2) − 2 = 10/3 (not equal).
- f(2) = (−8/3)*2 − 2 = −22/3 (not equal to g(−2)=4).

Therefore none of the four given statements is true.