QuizMultiple Choice

N/A — Exam

Question 7 • Algebra I

Which graph represents a reflection of f of x is equal to 1 third times 9 to the x th power across the x -axis?

Answer

Image with description A coordinate plane with an exponential curve. The x-axis is labeled from negative 2 to 8 in increments of 1 and the y-axis is labeled from negative 8 to 2 in increments of 1. The curve begins in the lower-left area of the plane near x equals 0 and y equals negative 7, and rises steeply with a positive slope before becoming nearly flat and approaching the x-axis from below as it extends to the right. The curve does not extend to the left of x equals 0.

Image with description A coordinate plane with an exponential curve. The x-axis is labeled from negative 7 to 3 in increments of 1 and the y-axis is labeled from negative 2 to 8 in increments of 1. The curve is nearly flat and very close to the x-axis across the left portion of the plane, then curves sharply upward with a steep positive slope in the right portion of the plane, rising past y equals 8 near x equals 1. The curve does not extend to the right of x equals 1.

Image with description A coordinate plane with an exponential curve. The x-axis is labeled from negative 8 to 2 in increments of 1 and the y-axis is labeled from negative 8 to 2 in increments of 1. The curve is nearly flat and very close to the x-axis across the left portion of the plane, then descends steeply with a steep negative slope in the right portion of the plane, falling past y equals negative 8 near x equals 0. The curve does not extend to the right of x equals 0.

Image with description A coordinate plane with an exponential curve. The x-axis is labeled from negative 2 to 8 in increments of 1 and the y-axis is labeled from negative 2 to 8 in increments of 1. The curve begins in the upper-left area of the plane near x equals 0 and y equals 7, and descends steeply with a negative slope, becoming nearly flat and approaching the x-axis as it extends to the right. The curve does not extend to the left of x equals 0.

Explanation

Reflecting a graph across the x-axis changes every y-value to its opposite. The reflected function is therefore y = −(1/3)·9^x, which stays below the x-axis, approaches 0 from below as x moves left, and decreases sharply as x moves right. Choice B, the curve that is nearly flat below the x-axis on the left and drops steeply on the right, has that shape.

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