Practice Test

Question 14 • Mathematics III

Which graph shows the solution to the equation? log sub 3 of open paren x plus 2 close paren is equal to 1

Answer

Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the y axis in the fourth quadrant. It passes through the points (1 comma 0), (3 comma 1) and increases as x increases. There is a line is parallel to the x axis and cuts the y axis at (0 comma negative 1).

Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (1 comma 1) and increases as x increases. There is a line parallel to the x axis and cuts the y axis at (0 comma 1).

Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma negative 1).

Image with description On a coordinate plane the x axis lists from negative 3 to 9 by 1 and y axis lists from negative 4 to 8 by 1. There is a smooth curve that approaches the line x equals negative 2 in the third quadrant. It passes through the point (negative 1 comma 0), (8 comma 1) and increases as x increases. There is a line that is parallel to the x axis and cuts the y axis at (0 comma 1).

Explanation

Rewrite the equation as a graph intersection: the curve is y = log₃(x + 2), and the horizontal line is y = 1. Solving log₃(x + 2) = 1 gives x + 2 = 3, so x = 1. Choice D shows the curve passing through (1, 1) and the line y = 1, so they intersect at the solution.

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