Chapter 4.2, Problem 58E

To determine

To make: conjectures about whether the two functions are equivalent using a graphing calculator.

Answer to Problem 58E

The function $f\left(x\right)$ and $g\left(x\right)$ are not same.

Explanation of Solution

Given information:

Given two functions are,

  $\begin{array}{l}h\left(x\right)={\left(x+2\right)}^5\\ h\left(x\right)=x^5+10x^4+40x^3+80x^2+64x\end{array}$

Calculation:

Input function $Y_1={\left(X+2\right)}^5$ using key $\left(X+2\right)\wedge 5$

  

Input function $Y_2=X^5+10X^4+40X^3+80X^2+64X$ using key,

  $X\wedge 5+10X\wedge 4+40X\wedge 3+80X\wedge 2+64X$

The display is shown below:

  

Now press the GRAPH key to obtain the graph.

  

Because both function have different graph, so the function $f\left(x\right)$ and $g\left(x\right)$ are not same.