Library of Functions. Constant -5 -4 -3 -2 -1 0 1 2 3 4 5 Intercepts? Domain? Range? Even, odd, neither? Increasing? Decreasing? Constant? Maxima? Minima?

Library of Functions

Constant

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

3)( xf

(Output is the same, no matter what the input is)

Identity (linear)

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

xxf )(

(Input equals output)

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Square (quadratic)

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

2)( xxf

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Square root

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

xxf )(

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Cube (cubic)

-10 -8 -6 -4 -2 0 2 4 6 8 10 x

f (x)

-8

-10

-6

-4

-2

2

4

6

8

10

3)( xxf

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Cube root

-10 -8 -6 -4 -2 0 2 4 6 8 10 x

f (x)

-8

-10

-6

-4

-2

2

4

6

8

10

3)( xxf

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Reciprocal

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

xxf

1)(

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Absolute value

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

||)( xxf

(Output is positive version of the input)

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Greatest integer

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

)int()( xxf

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

Circle

-5 -4 -3 -2 -1 0 1 2 3 4 5x

y

-4

-5

-3

-2

-1

1

2

3

4

5

222 ryx radiusr

Not a function!

922 yx

Semicircle

-5 -4 -3 -2 -1 0 1 2 3 4 5x

f (x)

-4

-5

-3

-2

-1

1

2

3

4

5

22)( xrxf

Intercepts?

Domain?

Range?

Even, odd, neither?

Increasing?

Decreasing?

Constant?

Maxima?

Minima?

29)( xxf

radiusr