Chapter 6.4, Problem 50E

(a)

To determine

To describe a transformation of the graph of $f$ that result in the graph of $g$ also explain if the value of $b$ is between 0 and 1 does it effects on the above transformation.

Answer to Problem 50E

The graph of $f$ is flipper over the $y$ -axis to obtain the graph of $g$ .

Explanation of Solution

Given information:

The given functions are $f\left(x\right)=b^x$ and its transformation function $g\left(x\right)={\left(\frac{1}{b}\right)}^x$ for $b=2$ and its graph is given below.

Calculation:

From the above graph of $f\left(x\right)=b^x$ and its transformed graph $g\left(x\right)={\left(\frac{1}{b}\right)}^x$ for $b=2$ , shows that graph $f$ reflect over $y-axis$ .

Also if the graph of $f\left(x\right)=b^x$ reflects over $y-$ axis then we get, then replace $x$ by $\left(-x\right)$ .

  $g\left(x\right)=f\left(-x\right)$

  $g\left(x\right)=b^{-x}$

  $g\left(x\right)={\left(\frac{1}{b}\right)}^x$