Exponential and Logarithmic Functions — Test

Question 13 • Algebra 2 with Probability

Which graph represents an exponential growth function?

Answer

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. The curve begins in the second quadrant, running nearly parallel and just above the negative x-axis asymptotically, with an arrowhead pointing directly to the left near "negative 9 comma 0 point 2". Moving right, it slowly curves upward, passes through "negative 1 comma 0 point 5", and crosses the y-axis at the y-intercept "0 comma 1". It then enters the first quadrant, curving sharply upwards and increasing rapidly through "1 comma 2", "2 comma 4", and terminates with an arrowhead pointing toward the top right near "3 comma 9".

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. The curve begins in the second quadrant, rising steeply upwards with an arrowhead pointing towards the top left near "negative 3 point 5 comma 9 point 5". As it moves right, it decreases rapidly, passing through "negative 1 comma 2", crossing the y-axis at the y-intercept " 0 comma 1", and flattening out significantly as it enters the first quadrant. It approaches the positive x-axis asymptotically, running nearly parallel and just above it, and ends with an arrowhead pointing directly to the right near "9 comma 0.3".

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. From the origin, double-headed arrow pointing up towards the origin and the curve bends downwards into the fourth quadrant and extends to the right, passing through approximately "1 comma negative 1", "4 comma negative 2", and "9 comma negetive 3", where it terminates near the right edge of the grid.

Image with description A Cartesian coordinate plane with horizontal x-axis and vertical y-axis, both grid-lined and ranges from negative 10 to 10 with an increment of 1. From the origin, double-headed arrow pointing down towards the origin and the curve rises slowly and extends to the right, passing through approximately "1 comma 1", "4 comma 2", and "9 comma 3", where it terminates near the right edge of the grid.

Explanation

An exponential growth graph increases slowly at first and then rises more and more rapidly as x increases. Choice C has that shape: it passes through points such as (0, 1), (1, 2), and (2, 4), with y-values doubling as x increases by 1. Choice A is a square-root graph, while D shows exponential decay.

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