Question

Which is the graph of g(x) = (0.5)x + 3 – 4 for an exponential function?

On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, negative 4).
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 3. It crosses the y-axis at (0, 3).
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, 4).
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 4. It crosses the y-axis at (0, 12).

Answer 1

Interpreting g(x) = (0.5)^{x+3} − 4 (the usual exponential form), the base 0.5 < 1 so the graph is decreasing. The vertical shift down 4 gives the horizontal asymptote y = −4. The y‑intercept is

g(0) = (0.5)^3 − 4 = 1/8 − 4 = −31/8 ≈ −3.875,

so the graph is decreasing with asymptote y = −4 and crosses the y‑axis just above −4. That matches the first choice (decreasing, asymptote y = −4); note the exact y‑intercept is (0, −31/8), not exactly (0, −4).