Question

Which is the graph of g(x) = (two-thirds) Superscript x – 2?

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)

Answer 1

The correct graph is the third one.

Reason: g(x) = (2/3)^x − 2 has base 0 < 2/3 < 1 so it is decreasing. Its horizontal asymptote is y = −2, and g(0) = 1 − 2 = −1, so the y‑intercept is (0, −1). As x → −∞, g(x) → +∞ (quadrant II), it crosses into quadrant III for some negative x, passes (0, −1), and for x > 0 stays negative approaching −2 (quadrant IV).