Chapter ISG, Problem 7.6.4P

To determine

To explain: The graph of function $y=2\left(2^x\right)$ is a graph of its parent function $y=2^x$ that rises more rapidly or shifted 2 units to the left.

Answer to Problem 7.6.4P

Jennifer is correct that the graph of $y=2\left(2^x\right)$ rises more rapidly.

Explanation of Solution

Given information: The transformed function $y=2\left(2^x\right)$ form its parent function $y=2^x$ . Jennifer claims that the transformed graph rises more rapidly and James claimed that graph shifted 2 units to the left.

The transformation of graph of exponential function from parent function to other equation can be drawn by the general equation:

  $y=a\cdot b^{x-h}+k$   ...... (1)

Here, $h$ shows horizontal shift, $k$ shows vertical shift and $a$ defines stretch or compression.

Compare the transformation function with the equation (1) to get,

  $\begin{array}{l}a=2\\ h=0\\ k=0\end{array}$

The graph cannot be shifted vertically 2 units to the left as $k=0$ . So, James claim is not correct.

The value of $a$ is greater than 1, so the graph stretch vertically. The graph increases more rapidly when stretched vertically.

Therefore, Jennifer is correct that the graph of $y=2\left(2^x\right)$ rises more rapidly.