AnswersAlgebraic ReasoningGraphing Logarithmic Functions

Graphing Logarithmic Functions — Quiz Answers

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What is the domain of y is equal to the log base 5 of x ?

A
all real numbers greater than 0
B
all real numbers
C
all real numbers less than 0
D
all real numbers not equal to 0
22
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A function is shown. f⁡(x)=log_9⁡(x) Aliyah translates the function down 2 units and right 5 units to create g⁡(x) What is g⁡(x) ? Enter your answer in the box.

Answer:

g(x)=log_9(x-5)-2

23

Which is the graph of a logarithmic function?

A
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).
B
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 and is symmetric about the line x equals 3. It has the minima at (3 comma 0) and passes through the points (5 comma 2) and (1 comma 2).
C
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 is a hyperbola that consists of two curves. One of the curves is in the first quadrant, passes through (3 comma 1), and approaches the positive direction of the x-axis, and line x equals 2. The other curve is the mirror image of the first curve about the line x equals 2 and passes through (1 comma 1).
D
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 positive slope that goes through (0 comma 0), and (5 comma 1).
24

The function y is equal to the log of x is translated 1 unit right and 2 units down. Which is the graph of the translated function?

A
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 (1 comma negative 4), moves up, and goes through (2 comma negative 2) and (9 comma negative 1).
B
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 (negative 1 comma negative 5), moves up, intersects the y-axis at (0 comma negative 2), and goes through (6 comma 0).
C
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 (negative 1 comma negative 1), moves up, and intersects the x-axis at (negative 1 comma 0). It further moves up, intersects the y-axis at (0 comma 2), and goes through (8 comma 4).
D
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 (1 comma negative 2 point 8), moves up, and intersects the x-axis at (1 comma 0). It goes to the right and passes through (2 comma 2) and (8 comma 4).

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