Question

Which graph represents a reflection of f(x) = One-tenth(10)x across the y-axis?

On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It goes through (1, negative 1).
On a coordinate plane, an exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (negative 1, 1).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (1, 1).
On a coordinate plane, an exponential function increases from quadrant 3 to quadrant 4 and approaches y = 0. It goes through (negative 1, negative 1).

Answer 1

Reflecting f(x) = (1/10)·10^x across the y-axis gives g(x) = f(−x) = (1/10)·10^{−x}. Since f(1)=1, g(−1)=1, and g is decreasing left→right with horizontal asymptote y=0 as x→∞, the matching description is:

"An exponential function decreases from quadrant 2 to quadrant 1 and approaches y = 0 in quadrant 1. It goes through (−1, 1)."

So the second graph.