Chapter 1.7, Problem 80E

(a)

To determine

To find: Whether the same graph is obtained or not.

Answer to Problem 80E

The graph after reversing the orders are not same.

Explanation of Solution

Given:

The given parent function is $f\left(x\right)=x^2$ .

Calculation:

Consider the given function is,

  $f\left(x\right)=x^2$

The transformed function $g\left(x\right)$ is derived by reflecting the function along the $x$ axis that is,

  $g\left(x\right)=-x^4$

Then shift the graph vertically 2 units upward that is,

  $g\left(x\right)=-x^4+2$

Thus, the transformed function is,

  $y=-x^4+2$

To obtain the other transformed function $g\left(x\right)$ by the following steps,

Vertically shift the graph two units in the upward direction and then reflect it across the $x$ axis,

  $y=-x^4-2$

Thus, the graph after reversing the orders are not same.

(b)

To determine

To find: Whether the same graph is obtained or not.

Answer to Problem 80E

The graph after reversing the orders are same as the order of transformations is important in determining the transformed function.

Explanation of Solution

Given:

The given transformed function is $g\left(x\right)=x^4$ .

Calculation:

Consider the given function is,

  $g\left(x\right)=x^4$

Shift the above function horizontally 3 units to the right and the reflect it across the x axis as,

  $g\left(x\right)=-{\left(x-3\right)}^4$

To obtain the transformed function $g\left(x\right)$ reflect the equation across the $x$ axis, that is,

  $g\left(x\right)=-x^4$

Shift the above function horizontally to the right by 3 units that is,

  $g\left(x\right)=-{\left(x-3\right)}^4$

This is because the order of transformation is important to determine the transformed function.