Question

Which of the following describes the transformation of g (x) = 3 (2) Superscript negative x Baseline + 2 from the parent function f (x) = 2 Superscript x?
reflect across the x-axis, stretch the graph vertically by a factor of 3, shift 2 units up
reflect across the y-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the x-axis, stretch the graph vertically by a factor of 2, shift 3 units up
reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up

Answer 1

"Reflect across the y-axis, stretch the graph vertically by a factor of 3, shift 2 units up."

Reason: 2^(−x) is f(−x) so the graph is reflected across the y-axis; multiplying by 3 gives a vertical stretch by 3; adding 2 shifts the graph up 2 units.