Practice Test

Question 9 • Mathematics III

Which of the following shows the graph of y is equal to the natural log of open paren negative 2 x close paren ?

Answer

Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant I, crosses the x axis at point 4 comma 0, decreases with x value. It approaches y axis in the quadrant IV.

Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant II, crosses the x axis at 0 point 5 comma 0, decreases with the increased value of x. It approaches y axis in the quadrant III.

Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant II, crosses the x axis at point negative 4 comma 0, decreases with the increased value of x. It approaches y axis in the quadrant III.

Image with description On a coordinate plane, the x and y axis ranges from negative 5 to 5 with increment of 1. There is a curved graph that starts from the quadrant I, crosses the x axis at 0 point 5 comma 0, decreases with x value. It approaches y axis in the quadrant IV.

Explanation

The logarithm is defined only when −2x > 0, so the graph lies to the left of the y-axis. Its x-intercept satisfies ln(−2x) = 0, which gives −2x = 1 and x = −0.5. As x approaches 0 from the left, ln(−2x) decreases without bound, so the graph drops in quadrant III near the y-axis. Choice B has these features and the intercept at (−0.5, 0).

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