Graphing Logarithmic Functions — Quiz

Question 10 • Algebraic Reasoning

Which is the graph of y is equal to negative log times open paren x minus 2 close paren plus 3 ?

Answer

Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 7 to 7 by 1. The graph has a curve that originates from (2 comma negative 4), moves up, intersects the x-axis at (3 comma 0), and goes through (9 comma 2).

Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 7 to 7 by 1. The graph has a curve that originates from (2 comma 0), moves up, and goes through (3 comma 3) and (9 comma 5).

Image with description On a coordinate plane, the x-axis lists negative 3 to 11 by 1, and the y-axis lists negative 5 to 9 by 1. The graph has a curve that originates from (2 comma 5), goes down, passes through (3 comma 3), and (11 comma 2).

Image with description On a coordinate plane, the x-axis lists negative 4 to 10 by 1, and the y-axis lists negative 7 to 7 by 1. The graph has a curve that starts from (2 comma 4), goes down, intersects the x-axis at (3 comma 0), and goes through (5 comma negative 1) and (9 comma negative 2).

Explanation

The graph of y = −log(x − 2) + 3 is shifted 2 units right and 3 units up, and the negative sign makes it decrease. At x = 3, log(3 − 2) = log(1) = 0, so y = 3. At x = 11, y = 3 − log(9), which is about 2.05 for common logarithms. Choice C decreases and passes through approximately (3, 3) and (11, 2), so it matches.

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