Vertical Stretches and Shrinks of Exponential Functions — Quiz

Question 4 • Algebra: Concepts and Connections

Which graph represents a function with an initial value of 1 half ?

Answer

Image with description On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.12), (0, 0.6), (1, 3).

Image with description On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.1), (0, 0.5), (1, 2.5).

Image with description On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.4), (0, 0.2), (1, 1).

Image with description On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through (negative 1, 0.08), (0, 0.4), (1, 2).

Explanation

The initial value of a function is its output when the input is 0, so look for the graph’s y-intercept. Since one half equals 0.5, the graph must pass through (0, 0.5). Choice A has that point; the other choices have different y-intercepts.

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