Chapter ISG, Problem 7.7STP

To determine

To find: The function that is drawn when shifted 2 units left and 5 units down form the graph of function $y=4^x$ .

Answer to Problem 7.7STP

The required function is $y=4^{x+2}-5$ .

Explanation of Solution

Given information: The graph of function $y=4^x$ is shifted 2 units to the left and 5 units downwards.

Calculation:

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.

The graph is shifted 2 units to the left and 5 units downwards. So,

  $\begin{array}{l}h=-2\\ k=-5\end{array}$

Substitute $-2$ for $h$ and $-5$ for $k$ in equation (1).

  $y=4^{x+2}-5$

Therefore, the required function is $y=4^{x+2}-5$ .