Translations of Exponential Functions — Quiz

Question 9 • Algebra: Concepts and Connections

Which is the graph of g of x is equal to 2 raised to the x minus 1 power plus 3 ?

Answer

Image with description On a coordinate plane, an exponential function has a horizontal asymptote at y = 3 and crosses the y-axis at (0 comma 3 point 5).

Image with description On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 3 and crosses the y-axis at (0 comma negative 2 point 5).

Image with description On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0 comma negative 1).

Image with description On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0 comma 7).

Explanation

For g(x) = 2^(x − 1) + 3, the +3 shifts the graph up, so its horizontal asymptote is y = 3. At x = 0, g(0) = 2^(−1) + 3 = 0.5 + 3 = 3.5, so the graph crosses the y-axis at (0, 3.5). This matches the graph in choice A.

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