Practice Test

Question 4 • Algebra I

Which is the graph of g of x is equal to 2 thirds to the x th power minus 2 ?

Answer

Image with description A coordinate plane displays the x-axis labeled from negative 4 to 4 in increments of 2 and the y-axis labeled from negative 4 to 4 in increments of 2. A decreasing curve passes through the labeled point 0 comma 2.25 and continues from the upper left toward the lower right. It passes through approximately the points negative 1 comma 3, 2 comma 1.1, and 4 comma 0.5.

Image with description A coordinate plane displays the x-axis labeled from negative 4 to 4 in increments of 2 and the y-axis labeled from negative 4 to 4 in increments of 2. A decreasing curve passes through the labeled point 0 comma 0.44 and continues from the upper left toward the lower right. It passes through approximately the points negative 4 comma 2, negative 2 comma 1, 2 comma 0.2, and 4 comma 0.1.

Image with description A coordinate plane displays the x-axis labeled from negative 4 to 4 in increments of 2 and the y-axis labeled from negative 4 to 4 in increments of 2. A decreasing curve passes through the labeled point 0 comma 3 and continues from the upper left toward the lower right. The graph passes through approximately the points negative 2 comma 4, 2 comma 2.4, and 4 comma 2.

Image with description A coordinate plane displays the x-axis labeled from negative 4 to 4 in increments of 2 and the y-axis labeled from negative 4 to 4 in increments of 2. A decreasing curve passes through the labeled point 0 comma negative 1 and continues from the upper left toward the lower right. The graph passes through approximately the points negative 4 comma 3, negative 2 comma 0.5, 2 comma negative 1.5, and 4 comma negative 2.

Explanation

For g(x) = (2/3)^x − 2, the y-intercept is g(0) = 1 − 2 = −1. Since the base 2/3 is between 0 and 1, the exponential decreases as x increases, and subtracting 2 shifts the graph down so its horizontal asymptote is y = −2. For example, g(−4) ≈ 3.06 and g(2) ≈ −1.56, matching choice D, the decreasing graph that passes through (0, −1).

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