Chapter 4.7, Problem 21E

To determine

To find: the correction of the error in graphing the function.

Answer to Problem 21E

The graph $g\left(x\right)$ shifted left by unit $b=4$ .

Explanation of Solution

Given:

  $g\left(x\right)={\left(x+4\right)}^4$ .

  

Concept used:

To move the function up add outside the function as:

  $f\left(x\right)+b$ is $f\left(x\right)$ moved up by $b$ units.

Moving the function down works the same way as $f\left(x\right)-b$ is $f\left(x\right)$ move down $b$ units.

To shift the function left, add inside the function’s argument:

  $f\left(x+b\right)$ gives $f\left(x\right)$ shifted $b$ units to the left.

Shifting to the right work the same way as $f\left(x-b\right)$ is $f\left(x\right)$ shifted $b$ units to the rights.

A function $f\left(x\right)$ , a new function $g\left(x\right)=kf\left(x\right)$ , where $a$ is the constant, is a vertical stretch or vertical compression of the function $f\left(x\right)$ .

If $a>1$ then graph will be stretched.

If $0<a<1$ , then the graph will be compressed.

If $a<0$ ,then there will be combination of a vertical stretch or compression with a vertical reflection.

The graph can be sketch using graphing calculator like Desmos graphing calculator.

Calculation:

According to the given:

  $g\left(x\right)={\left(x+4\right)}^4$ .

The graph will parabola type since, the power of the equation is even.

For the function like $f\left(x+b\right)$ gives $f\left(x\right)$ shifted $b$ units to the left.

Here $b=4$ .

The graph Is shifted $4$ unit towards the left and the graph can be plot as:

  

the graph of $g\left(x\right)$ is represented by the red curve.

Hence, the graph $g\left(x\right)$ shifted left by unit $b=4$ .