Logarithmic Functions Transformation (2A.5A)

If $f\left(x\right)=\log x$  is changed to $g\left(x\right)=-\frac{1}{2}f\left(x+4\right)+3$  , how is the graph transformed?

• The graph of f(x) is vertically stretched by a factor of 2, reflected across the x-axis, then translated 3 units up and 4 units left to create the graph of g(x).

• The graph of f(x) is vertically stretched by a factor of 2, reflected across the x-axis, then translated 3 units down and 4 units right to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of 1/2, reflected across the x-axis, then translated 3 units up and 4 units left to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of 1/2, reflected across the x-axis, then translated 3 units down and 4 units left to create the graph of g(x).

If $f\left(x\right)=\log x$ is changed to $g\left(x\right)=f\left(-\left(x+3\right)\right)+2$  , how is the graph transformed?

• The graph of f(x) is reflected across the y-axis, then translated 3 units right and 2 units up to create the graph of g(x).

• The graph of f(x) is reflected across the x-axis, then translated 3 units right and 2 units up to create the graph of g(x).

• The graph of f(x) is reflected across the y-axis, then translated 3 units left and 2 units up to create the graph of g(x).

• The graph of f(x) is reflected across the x-axis, then translated 3 units left and 2 units up to create the graph of g(x).

If $f\left(x\right)=\log x$ is changed to $g\left(x\right)=3f\left(x-4\right)$  , how is the graph transformed?

• The graph of  f(x) is vertically compressed by a factor of 3 and translated 4 units left to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of 3 and translated 4 units right to create the graph of g(x).

• The graph of f(x) is vertically stretched by a factor of 3 and translated 4 units left to create the graph of g(x).

• The graph of f(x) is vertically stretched by a factor of 3 and translated 4 units right to create the graph of g(x).

If $f\left(x\right)=\log x$ is changed to $g\left(x\right)=f\left(x-5\right)-4$  , how is the graph transformed?

• The graph of f(x) is translated 5 units left and 4 units down to create the graph of g(x).

• The graph of f(x) is translated 5 units left and 4 units up to create the graph of g(x).

• The graph of f(x) is translated 5 units right and 4 units down to create the graph of g(x).

• The graph of f(x) is translated 5 units right and 4 units up to create the graph of g(x).

If $f\left(x\right)=\log x$ is changed to $g\left(x\right)=\frac{1}{3}f\left(x\right)-2$  , how is the graph transformed?

• The graph of f(x) is vertically stretched by a factor of 3 and translated 2 units up to create the graph of g(x).

• The graph of f(x) is vertically stretched by a factor of 3 and translated 2 units down to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of  1/3 and translated 2 units up to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of 1/3 and translated 2 units down to create the graph of g(x).

If $f\left(x\right)=\log x$ is changed to $g\left(x\right)=3f\left(x-4\right)-2$  , how is the graph transformed?

• The graph of f(x) is vertically stretched by a factor of 3 and translated 2 units up and 4 units right to create the graph of g(x).

• The graph of f(x) is vertically stretched by a factor of 3 and translated 2 units down and 4 units right to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of 3 and translated 2 units up and 4 units left to create the graph of g(x).

• The graph of f(x) is vertically compressed by a factor of 3 and translated 2 units down and 4 units left to create the graph of g(x).

If $f\left(x\right)=\log x$ is changed to $g\left(x\right)=f\left(x\right)-3$  , how is the graph transformed?

• The graph of f(x) is shifted 3 units up to create the graph of g(x).

• The graph of f(x) is vertical stretched than the graph of g(x).

• The graph of f(x) is shifted 3 units down to create the graph of g(x).

• The graph of f(x) is vertical compressed than the graph of g(x).

The graph of  $f\left(x\right)=\log x$ is shown. Which statement about the relationship between the graph of f (x) and the graph of  $g\left(x\right)=\frac{1}{7}\log\ \left(x\right)$  is true?

• The graph of g (x) is vertical compressed by a factor of 1/7 to the graph of f(x).

• The graph of g (x) is vertical stretched by a factor of 1/7 to the graph of f(x).

• The graph of g(x) is 7 units below the graph of f(x).

• The graph of g(x) is 7 units above the graph of f(x).

Which statement best describes the effects on the graph of  $f\left(x\right)=\log x$ when f(x) is replaced by $-f\left(\frac{1}{2}\left(x-3\right)\right)-5$  is true?

• The graph is reflected over the y-axis, horizontally stretched by a scale factor of 2, horizontally shifted 3 units to the right, and vertically shifted 5 units up.

• The graph is reflected over the x-axis, horizontally compressed by a scale factor of  1/2, horizontally shifted 3 units to the right, and vertically shifted 5 units up.

• The graph is reflected over the y-axis, horizontally compressed by a scale factor of 1/2, horizontally shifted 3 units to the right, and vertically shifted 5 units down.

• The graph is reflected over the x-axis, horizontally stretched by a scale factor of 2, horizontally shifted 3 units to the right, and vertically shifted 5 unit down.

Which statement best describes the effects on the graph of  $f\left(x\right)=\log x$ when f(x) is replaced by $f\left(3\left(x-8\right)\right)-5$  is true?

• The graph is horizontally compressed by a scale factor of 1/3 horizontally shifted 8 units to the right, and vertically shifted 5 units down.

• The graph is vertically stretched by a scale factor of 3, horizontally shifted 8 units to the right, and vertically shifted 5 units down.

• The graph is vertically stretched by a scale factor of 3, horizontally shifted 8 units to the left, and vertically shifted 5 units up.

• The graph is horizontally compressed by a scale factor of 1/3, horizontally shifted 8 units to the left, and vertically shifted 5 units up .