N/A — Exam

Question 37 • Algebra II

Which graph shows the solution to the equation? log sub 3 of open paren x plus 3 close paren is equal to log sub 0 point 3 of open paren x minus 1 close paren

Answer

Image with description On a coordinate plane the x axis lists from negative 7 to 13 by 1 and y axis lists from negative 10 to 10 by 1. There are two curved graphs. One of the curves starts from third quadrant, passes through (negative 1 comma 4), (0 comma 5), and (1 comma 6). It increases for negative values of x changes its direction at point (0 comma 5) and then again increases for positive values of x. The other curve passes through (10 comma 1), decreases with x value and passes through (1 comma 0) and approaches negative part of the y axis.

Image with description On a coordinate plane the x axis lists from negative 7 to 13 by 1 and y axis lists from negative 10 to 10 by 1. Two curved graphs are drawn. One of them approaches the line x equal 1 in the second quadrant and increase as x increases. It passes through points (2 comma 0) and (10 comma 1). The other curve approaches x equals negative 3 in the third quadrant and passes through (negative 2 comma 0) and (6 comma 1).

Image with description On a coordinate plane the x axis lists from negative 7 to 13 by 1 and y axis lists from negative 10 to 10 by 1. There are two curved graphs drawn. One of the curve approaches the x equal 1 in the first quadrant and decrease as x increases. It passes through point (2 comma 0). The other curve approaches x equals negative 3 in the third quadrant and passes through (negative 2 comma 0) and (0 comma 1).

Image with description On a coordinate plane the x axis lists from negative 7 to 13 by 1 and y axis lists from negative 10 to 10 by 1. There is a curved graph and a straight line. The graph approaches the y axis in the first quadrant and decreases as x increases. It passes through points (1 comma 0) and (10 comma negative 1). The line is parallel to y axis and cuts the x axis at (3 point 3 comma 0).

Explanation

The graph of y = log₃(x + 3) is increasing, has a vertical asymptote at x = −3, and crosses the x-axis at x = −2. The graph of y = log₀.₃(x − 1) is decreasing because its base is between 0 and 1; it has a vertical asymptote at x = 1 and crosses the x-axis at x = 2. Choice C shows both graphs with these features.

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