Library of Functions. Constant -5 -4 -3 -2 -1 0 1 2 3 4 5 Intercepts? Domain? Range? Even, odd,...
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Transcript of Library of Functions. Constant -5 -4 -3 -2 -1 0 1 2 3 4 5 Intercepts? Domain? Range? Even, odd,...
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