Exponential and Logarithmic Functions — Test

Question 18 • Algebra 2 with Probability

Which graph represents an exponential function?

Answer

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The curve originate from the origin and passes through the points 1 comma 3, 2 comma 4, 5 comma 7, and 7 comma 8 in the first quadrant. The arrow is present on both end of curve.

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The graph is made up of two different curves that do not meet. One of the curve decreases rapidly in the second quadrant and passes through the point 0 comma 1 and it goes towards the x axis in first quadrant. The other curve cuts the x axis at point negative 4 comma 0 and then goes rapidly towards the negative side of the y axis in the third quadrant. The arrow is present on both end of two curve.

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The curve passes through the point 0 comma 1, 1 comma 3 and 2 comma 9. It increases rapidly in the first quadrant as x increase and goes towards the y axis as x decreases in the second quadrant. The arrow is present on both end of curve.

Image with description On a coordinate plane, the x and y axes ranges from negative 10 to 10 with an increment of 1. The curve passes through the point negative 2 comma negative 4, the origin, and 2 comma 4. The curve decreases rapidly in the first and the third quadrant and changes direction at the origin. The arrow is present on both end of curve.

Explanation

An exponential function changes by a constant multiplicative factor when x increases by 1. In graph D, the y-values go from 1 at x = 0 to 3 at x = 1, then to 9 at x = 2, multiplying by 3 each time. This matches an exponential function such as y = 3^x, so the correct choice is the graph passing through (0, 1), (1, 3), and (2, 9).

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