Exponential and Logarithmic Functions — Test

Question 9 • Algebra 2 with Probability

Which graph represents an exponential function?

Answer

Image with description On a coordinate plane, the graph is made up of two different curves that do not meet. The x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. The upper left curve is located entirely within the second quadrant. It extends from the far left, approaching the horizontal line y = 2 from above, and rises steeply upwards as it approaches the vertical line x = negative 2 from the left. It passes through (negative 3 comma 3). The lower right curve starts in the third quadrant, approaching the vertical line x = negative 2 from the right. It passes through the point (negative 1 comma 1) and then extends into the first quadrant, approaching the horizontal line y = 2 from below.

Image with description On a coordinate plane, the curve is symmetric about y axis in the third and the fourth quadrant. The x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. A parabola opens downwards with its vertex at the origin (0 comma 0). The parabola passes through points such as (1 comma negative 1), (2 comma negative 4), (negative 1 comma negative 1), and (negative 2 comma negative 4).

Image with description On a coordinate plane, the x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. The curve passes through the points (negative 1 comma 0) and (0 comma 1). From (negative 1 comma 0), the curve extends downwards and to the left into the third quadrant, with an arrow indicating it continues indefinitely. From (negative 1 comma 0), the curve also extends upwards and to the right, passing through (0 comma 1) and approaching the horizontal line y = 2 as x increases, with an arrow indicating it continues indefinitely in the first quadrant.

Image with description On a coordinate plane, the x axis is labeled from negative 10 to 10, and the y axis is labeled from negative 10 to 10. The curve originates at the point (negative 2 comma 0) on the x axis. It extends upwards and to the right, passing through the points (negative 1 comma 1), (2 comma 2), and (7 comma 3), and continues indefinitely into the first quadrant.

Explanation

An exponential graph has a curved shape and typically approaches a horizontal asymptote on one end. In A, the curve approaches the horizontal line y = 2 as x increases, while extending downward without bound to the left, which is consistent with a transformed exponential function. B is a parabola, C has the shape of a square-root function, and D has separate branches with a vertical asymptote.

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