Question

Make a rough sketch by hand of the graph of the function. Use the graphs given in Figures 3 and 15 and, if necessary, the transformations of Section 1.3.

12. \(y = {{\bf{4}}^{x + {\bf{2}}}}\)

Short answer

The graph of the function \(y = {4^{x + 2}}\) is obtained from the graph of \(y = {4^x}\) after the following transformation:

• Shift the graph 2 units to the left.

Step-by-step solution

Write the transformation to find the graph of \(y = {{\bf{4}}^{x + {\bf{2}}}}\) 

The graph of the function \(y = {4^{x + 2}}\) is obtained from the graph of \(y = {4^x}\) after the following transformation:

• Shift the graph 2 units to the left.

Sketch the graph of transformation from \(y = {{\bf{4}}^x}\) and \(y = {{\bf{4}}^{x + {\bf{2}}}}\)

The figure below represents the graph of \(y = {4^x}\):

The figure below represents the graph of \(y = {4^{x + 2}}\):

Thus, the graph of the function is obtained.