Chapter SH, Problem 7.24EP

To determine

To represent the $f(x)=9^x$translated up 2 units and left 4 uints.

Answer to Problem 7.24EP

Transformation of graph is $g(x)=9^{x+5}+2$ .

  

Explanation of Solution

Given information:

  $f(x)=9^x$

Calculation:

Let $g(x)$be the indicated transformation of $f(x)$ .

In general, transtated up of $f(x)$by factor a .

  $g(x)\to f(x)+a$

Then, transtated up of f(x) by factor 2 units .

  $f(x)=9^x+2$

In general, translation of $f(x)$left by b units.

  $g(x)\to f(x+b)$

Then, translation of $f(x)$left by up 5 units.

  $f(x+5)=9^{x+5}$

Then, required transformation is

  $g(x)=9^{x+5}+2$

Transformed graph, $g(x)$ of $f(x)$ is given below

  

Hence, the transformation of is $g(x)=9^{x+5}+2$ .