Graphing Logarithmic Functions — Quiz

Question 9 • Mathematics III

Which is the graph of a logarithmic function?

Answer

Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a hyperbola. The curve above the x-axis has a vertex at (4 comma 1) and the curve below the x-axis has a vertex at (2 comma negative 1).

Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a curve that originates from (0 comma negative 2 point 5), moves up, and intersects the x-axis at (1 comma 0). It passes through (3 comma 1) and (8 comma 2).

Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a parabola that opens upwards, with a vertex at (4 comma 0). It passes through (2 comma 4) and (6 comma 4).

Image with description On a coordinate plane, the x-axis lists negative 2 to 8 by 1, and the y-axis lists negative 5 to 5 by 1. The graph has a straight line with a negative slope that has an x-intercept at (3 comma 0) and a y-intercept at (0 comma 3).

Explanation

A logarithmic graph can increase while rising more slowly as x gets larger, and it has a vertical asymptote at x = 0. Choice C shows that shape: it crosses the x-axis at (1, 0), then rises through (3, 1) and (8, 2). The other graphs are a hyperbola, a straight line, and a parabola, so they are not logarithmic.

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