Question

Two functions are defined as shown.

f(x) = f(x) equals negative StartFraction 1 Over 2 EndFraction x minus 2. x – 2

g(x) = –1

Which graph shows the input value for which f(x) = g(x)?

A coordinate grid with two lines. One line labeled f(x) passes through (negative 2, 3), (0, 1), and point (2, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 1), (0, negative 1), and point (3, negative 1).

A coordinate grid with two lines. One line labeled f(x) passes through (negative 4, 0), point (negative 2, 0), and (0, negative 2). The second line is labeled g(x) and passes through (negative 3, negative 1), (0, negative 1), and point (3, negative 1).

A coordinate grid with two lines. One line labeled f(x) passes through (negative 4, 1), (negative 2, 0), and point (1.5, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 1), (0, negative 1), and point (1.5, negative 1).

Answer 1

Answer: the third graph.

Reason: Solve f(x) = g(x). From the graph f has slope -1/2 and goes through (-2,0) and (-4,1), so its equation is f(x) = -1/2 x - 1. Set -1/2 x - 1 = -1 => x = 0. The third graph shows f and g meeting at (0, -1).