1. Date Library of Functions
Page #
Learning Targets –
I can graph the functions listed in the library of functions.
I can evaluate a piecewise function for specific values.

2. There are certain properties that apply to the graphs of functions
There are certain properties that apply to the graphs of functions. We will look at some new functions and review some of the functions we are familiar with.

3. Square Root Function x Y 1 4 9 16

4. Properties of Square Root Function *The domain and range
are the set of nonnegative
real numbers.
*The x-intercept and the
y-intercept are at (0, 0).
*The function is neither
even nor odd.
*It is increasing on the
interval (0, ).
*It has a minimum value
of 0 at x = 0.

5. Cube Root Function x Y -8 -1 1 8

6. Properties of Cube Root Function *The domain and range
are the set of all real
numbers.
*The x-intercept and the
y-intercept are at (0, 0).
*The function is symmetric
with respect to the origin.
It is an odd function.
*It is increasing on the
interval (-, ).
*It does not have a local
minimum or maximum value.

7. Absolute Value Functionx Y -2 -1 1 2

8. Absolute Value Function
* The domain is the set
of all real numbers. The
range of f is
* The x-intercept for the
graph of is 0.
The y-intercept of
is also 0.
*The graph is symmetric with
respect to the y-axis. The
function is even.
* It is decreasing on the
interval (-, 0). It is increasing
on the interval (0, ).
* It has a local minimum of 0 at x = 0.

9. f(x) = b, where b is a real number
Constant Function
f(x) = b, where b is a real number
The domain of a constant
function is the set of all
real numbers; its range is
the set consisting of a
single number b.

10. Identity Function
f(x) = x
The domain and range
of the identity function
is the set of all real
numbers. Its graph has
a slope of 1 and a
y-intercept of 0.

11. Square Function f(x) = x2
The domain of the square
function is the set of all
real numbers; its range is
the set of nonnegative
real numbers. The graph
of the square function is a
parabola whose intercept
is at (0, 0). The square function
Is an even function that is
decreasing on the interval
(-, 0) and increasing on the
interval (0, )

12. Cube Function f(x) = x3 The domain and range of the cube function is
the set of all real numbers.
The intercept of the graph
is at (0, 0). The cube function
is an odd function and is
increasing on the interval
(-, ).

13. Cube Root Function The domain and the range
of the cube root function are
the set of all real numbers.
The intercept of the graph is
at (0, 0).
The cube root function is an
odd function that increasing
on the interval (-, ).

14. Reciprocal Function
*The domain and range
of the reciprocal function
are the set of all nonzero
real numbers.
*The graph has no
intercepts.
*The reciprocal function is
decreasing on the intervals
(-, 0) and (0, ).

15. Evaluating Piecewise Functions
Sometimes a function is defined differently on different parts of its domain. The absolute value function is actually defined by two equations: f(x) = x if x > 0 and f(x) = -x if x < 0.

16. 1. For the function f defined as
Evaluate f(-2), f(1), and f(3).

17. 2. For the function f defined as
Evaluate f(-4), f(-1), and f(6).

18. 3. For the function f defined as
Evaluate f(-6), f(0), and f(9).

19. 4. For the function f defined as
Find f(0), f(1), and f(2).