Chapter 11, Problem 26SGA

To determine

Graph the exponential function or inequality.

Answer to Problem 26SGA

  

Explanation of Solution

Given information:

  $y<2^{x+2}$

Calculation:

Here, we will consider the following:

  $y<2^{x+2}$

Now, we will find the values of $x$ for different values of $y$ :

  $\begin{array}{ll}x\hfill & y\hfill \\ -5\hfill & -0.125\hfill \\ -4\hfill & -0.25\hfill \\ -3\hfill & -0.5\hfill \\ -2\hfill & 1\hfill \\ -1\hfill & 2\hfill \\ 0\hfill & 4\hfill \\ 1\hfill & 8\hfill \\ 2\hfill & 16\hfill \\ 3\hfill & 32\hfill \\ 4\hfill & 64\hfill \\ 5\hfill & 128\hfill \end{array}$

Now, we will plot the points on the graph. Connect the points to graph the function $y<2^{x+2}$ .

  

Now, we will consider the point $\left(1,1\right)$ and will decide the area of shade:

  $\begin{array}{l}y<2^{x+2}\\ 1<2^{1+2}\\ 1<2\\ 1<8\\ \therefore True\end{array}$

Hence, the results are shown in the above graph.