Practice Test

Question 10 • Mathematics 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 On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0 comma 3).

Image with description On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0 comma 2 point 25).

Image with description On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0 comma 0 point 44).

Image with description On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0 comma negative 1).

Explanation

For g(x) = (2/3)^x − 2, the base is between 0 and 1, so the exponential decreases as x increases. At x = 0, g(0) = 1 − 2 = −1, and as x gets larger, the graph approaches the horizontal asymptote y = −2. For sufficiently negative x, the function is positive; it then passes through the negative y-values and approaches −2, matching the graph described in choice D.

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