Question

In elementary school, we learned about opposite operations such as addition and subtraction, and multiplication and division In both of these cases, one operation "undoes " the other . In this course, we'll begin to explore "opposite" function types. For example think about a quadratic function and its key features. What key features do you think its opposite function will have ? Why? (SHORT ANSWERS ONLY)

Answer 1

Given: a quadratic function and its key features

To Determine: what key features its opposite function will have

Solution:

The main features of the opposite function of the quadratic equation are reflection and symmetrical

Step-by-step explanation:

The opposite function or inverse functions are reflections of each other over the line y = x.

We will find the inverse by switching x and y in the equation. For example:

`f(x)=x^2+5`

The inverse would be

`\begin{gathered} f(x)-5=x^2 \\ x=\sqrt[]{f(x)-5} \\ f^(-1)(x)=\sqrt[]{f(x)-5} \end{gathered}`

Once you graph those two functions, you'll see that they're symetrical that has y=x line as its middle line

Answer Summary:

The main features of the opposite function of the quadratic equation are

Reflection and Symmetrical