The discriminant is less than 0

The discriminant equals 0

The discriminant is greater than 0

The discriminant is an imaginary number

Each y coordinate is multiplied by a constant

A constant is added to each y coordinate

Each x coordinate is multiplied by a constant

A constant is added to each x coordinate

The y coordinates change signs

The x coordinates change signs

Both x and y coordinates change signs

A constant is added to each x coordinate

$$f^{-1}\left(x\right)=5x+3$$

$$f^{-1}\left(x\right)=3x-5$$

$$f^{-1}\left(x\right)=\frac{1}{3x+5}$$

$$f^{-1}\left(x\right)=\frac{x-5}{3}$$

$$f_1\left(x\right)=\frac{1}{x}$$

$$f_2\left(x\right)=\frac{3x-5}{4x+8}$$

$$f_3\left(x\right)=\frac{x^2+3x-1}{x-7}$$

$$f_4\left(x\right)=\frac{x-7}{x^2+3x-1}$$

It is a torture device

It is used to find the roots (or zeros) of a function

It is used to identify when a function has a positive slope or a negative slope

It is used to keep track of when a function's outputs are positive or negative

Multiply the two functions

It is the same as dividing: $$\frac{f\left(x\right)}{g\left(x\right)}$$

Use $$g\left(x\right)$$ as the input of $$f\left(x\right)$$

Use $$f\left(x\right)$$ as the input of $$g\left(x\right)$$

Get the value of $$f\left(4\right)$$ . Use it as input for $$f$$ . The output is the answer.

Get the value of $$f\left(4\right)$$ . Then square it to get the answer.

Get the value of $$f\left(4\right)$$ . That is the answer.

Get the value of $$f\left(4\right)$$ . Then find its reciprocal to get the answer.

No, if a graph is self-symmetric with respect to the line $$y=x$$ , then it would fail the vertical line test.

Yes, but $$y=x$$ is the only valid example.

Yes, there are many examples of self-inverse functions.

Yes, each different type of function family has self-inverse functions.