Chapter 7.6, Problem 35PPS

To determine

Find the translation of the function.

Answer to Problem 35PPS

The graph of $g\left(x\right)=-0.7{\left(1.26\right)}^{x+4}-5$ shows reflection with respect to $x-axis$ , shifted $4-unit$ with respect to negative $x-axis$ , shifted $5-unit$ with respect to negative $y-axis$ and the graph shows vertical compress by $factor-0.7$

Explanation of Solution

Given information:

It is given in the question that, $g\left(x\right)=-0.7{\left(1.26\right)}^{x+4}-5$

Since, $g\left(x\right)=-0.7{\left(1.26\right)}^{x+4}-5$ so let the parent function be $f\left(x\right)={\left(1.26\right)}^x$

By multiplying $"-0.7"$ , adding $"4"$ in the exponential part then and subtracting $"5"$ in the non-exponential part of $f\left(x\right)$ then $g\left(x\right)=-0.7{\left(1.26\right)}^{x+4}-5$ is arrived

So, by the concept of translation of graph when something negative quantity is multiplying in the function then the graph shows reflection with respect to $x-axis$ , when some quantity is adding in the exponential part of function then the graph shifted with respect to negative $x-axis$ , when some quantity is subtracting in the non-exponential part of function then the graph shifted with respect to negative $y-axis$ and when some quantity which is $>0and<1$ is multiply to the function then the graph shows vertical compress.

So, the graph of $g\left(x\right)=-0.7{\left(1.26\right)}^{x+4}-5$ shows reflection with respect to $x-axis$ , shifted $4-unit$ with respect to negative $x-axis$ , shifted $5-unit$ with respect to negative $y-axis$ and the graph shows vertical compress by $factor-0.7$