Chapter 7.6, Problem 76PFA

To determine

To identify the function which represents the function $g(x)$ for the given graph

Answer to Problem 76PFA

B

Explanation of Solution

Given:

  

From the visual inspection of the given graph, it is clear that $g(x)$ is the vertically shifted graph of parent function $f(x)$ and at $x=0$ , $g(0)=-4$

Hence, $f(x)=b^x$

In order to obtain the function $g(x)$ , put $g(0)=-4$ .

  $\Rightarrow g(x)=f(x)+b$

  $\Rightarrow g(x)={1.5}^x+b$

Calculation:

Let,

  $\Rightarrow g(x)={1.5}^x+b\mathrm{..............}(i)$

Now, putting $x=0$ in equation ( i ),

  $\begin{array}{l}\Rightarrow g(0)={1.5}^0+b\\ \Rightarrow -4=1+b\\ \Rightarrow b=-5\end{array}$

The obtained function is: $g(x)={1.5}^x-5$

Conclusion:

Hence, the required function is: $g(x)={1.5}^x-5.$