91Ó°ÊÓ

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function \(f .\) $$ g(x)=4 f(x) $$

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function \(f .\) $$ g(x)=6 f(x) $$

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function \(f .\) $$ g(x)=f(5 x) $$

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function \(f .\) $$ g(x)=f(2 x) $$

For the following exercises, describe how the graph of each function is a transformation of the graph of the original function \(f .\) $$ g(x)=3 f(-x) $$

For the following exercises, write a formula for the function \(g\) that results when the graph of a given toolkit function is transformed as described. The graph of \(f(x)=|x|\) is reflected over the \(y\) -axis and horizontally compressed by a factor of \(\frac{1}{4}\)

For the following exercises, write a formula for the function \(g\) that results when the graph of a given toolkit function is transformed as described. The graph of \(f(x)=\sqrt{x}\) is reflected over the \(x\) -axis and horizontally stretched by a factor of 2.

For the following exercises, write a formula for the function \(g\) that results when the graph of a given toolkit function is transformed as described. The graph of \(f(x)=\frac{1}{x^{2}}\) is vertically compressed by a factor of \(\frac{1}{3},\) then shifted to the left 2 units and down 3 units.

For the following exercises, write a formula for the function \(g\) that results when the graph of a given toolkit function is transformed as described. The graph of \(f(x)=\frac{1}{x}\) is vertically stretched by a factor of \(8,\) then shifted to the right 4 units and up 2 units.

For the following exercises, write a formula for the function \(g\) that results when the graph of a given toolkit function is transformed as described. The graph of \(f(x)=x^{2}\) is vertically compressed by a factor of \(\frac{1}{2},\) then shifted to the right 5 units and up 1 unit.