Practice Exam

Question 8 • Algebra II

Which of the following shows the graph of y is equal to negative 2 to the x th power minus 1 ?

Answer

Image with description On a coordinate plane, the curve approaches x axis for negative values of x in the third quadrant. It passes through (negative 1 comma negative 1), (0 comma negative 2), (1 comma negative 4), and decreases rapidly in the fourth quadrant.

Image with description On a coordinate plane, the curve approaches x axis for negative values of x in the third quadrant. It passes through (1 comma negative 1), (2, comma negative 2), (3 comma negative 4), and decreases rapidly in the fourth quadrant.

Image with description On a coordinate plane, the curve approaches the line y equals 1 for negative values of x in the second quadrant. It passes through the origin, (1 comma negative 1), (2 comma negative 3), and decreases rapidly in the fourth quadrant.

Image with description On a coordinate plane, the curve approaches the line y equals negative 1 for negative values of x in the third quadrant. It passes through (0 comma negative 2), (1 comma negative 3), (2 comma negative 5), and decreases rapidly in the fourth quadrant.

Explanation

For y = −2^x − 1, when x = 0, y = −1 − 1 = −2; when x = 1, y = −2 − 1 = −3; and when x = 2, y = −4 − 1 = −5. As x becomes very negative, 2^x approaches 0, so the graph approaches y = −1. Choice D shows these points and this horizontal asymptote.

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