For each graph, an original function has undergone a transformation. Draw the graph of the transformed function if it has been shifted left 3, stretched vertically by a factor of 2, and shifted down 4.
$f(x)=2^x$
$g(x)=x^2$
$h(x)=\sqrt{x}$
Problem 2
A graph has been transformed from an original function according to the following transformations. Select all of the transformations that affect the input of the function:
Vertical stretch by a factor of 3
Horizontal stretch by a factor of \(\frac12\)
Reflect over the \(y\)-axis
Reflect over the \(x\)-axis
Shift left 4
Shift down 6
Problem 3
Here is a graph of \(f(x)=x^3\).
Draw the graph of the new function after the following transformations:
Function \(g\) has been translated left 2, stretched vertically by a factor of \(\frac12\), and translated down 4.
Function \(h\) has been reflected over the \(x\)-axis, stretched horizontally by a factor of 2, and translated up 3.
Function \(k\) has been stretched horizontally by a factor of 3, shifted left 3, and shifted up 3.
Problem 4
Each of the graphs have been transformed from the original function \(y=\sqrt{x}\). Match each graph with the transformation that was applied.