Base e — Quiz

Question 8 • Precalculus

Which of the following shows the graph of y is equal to 2 ln x ?

Answer

Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends horizontally along the negative x-axis, curves upward to pass through 0 comma 2, and rises sharply before 1 on the x-axis into the first quadrant.

Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends horizontally along the negative x-axis, curves upward through 0 comma 1, and rises sharply before 1 on the x-axis into the first quadrant.

Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends upward along the negative y-axis from near negative 5, passes through the horizontal x-axis at 1 comma 0, and rises gradually through the first quadrant passing through approximately 3 comma 2.

Image with description A coordinate plane with a horizontal x-axis and vertical y-axis both labeled from negative 5 to 5 in increments of 1. A curve extends upward from 0 comma negative 1 on the vertical y-axis, crosses the horizontal x-axis between the origin and 1, and rises gradually through the first quadrant passing through 4 comma 2.

Explanation

The graph of y = 2 ln x is defined only for x > 0 and has a vertical asymptote at x = 0. It crosses the x-axis at x = 1 because ln 1 = 0, and it passes through about (3, 2) because 2 ln 3 is approximately 2.2. Choice D shows these features.

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