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).

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

Answer 1

Set f(x) = g(x):

-1/2 x - 2 = -1
=> -1/2 x = 1
=> x = -2.

So the input value is x = -2, i.e. the intersection point is (-2, -1). Choose the graph that shows the two lines meeting at (-2, -1). (None of the four listed option descriptions shows the lines meeting at (-2, -1).)