Date:
Objective:
A)Functions
A ___________ is a mapping or ____________ of __________ values with _________ values. The set of
_________ values = ___________. The set of ____________ values = ___________.
A relation is a ______________ provided that there is _______ output for ____________ input.
Look at this example:
Input
Output
In an abstract way, you can think of it as no person can be in two places at once. Simply, there
_______________ be ________ of the __________ values in the __________ column that lead to a
____________ number in the __________ column.
Is a function always a relation? Is a relation always a function?
Since we now know what a function is, tell if the following relations are functions. If not, state why. Also, state
the domain and range for each relation.
a) Input Output
b) Input Output
c) Input Output
D:
R:
D:
R:
D:
R:
A relation can be _______________ by a set of ___________ _________ that looks like (x,y). The _________
number is always the ___-coordinate. The ___________ number is always the ____-coordinate. To graph a
relation, _________ ordered pairs on the _____________ plane. The coordinate plane is made up of
_________ quandrants.
Quadrant I – (+,+)
Quadrant II – (-,+)
Quadrant III – (-,-)
Quadrant IV – (+,-)
x and y are both __________
x is _______, y is _________
x and y are both __________
x is _______, y is _________
x-axis is the ______________ axis (left/right)
y-axis is the ______________ axis (up/down)
Looking at examples b and c, write the relation as a set of ordered pairs. Then graph.
(x,y)
(x,y)
Look at the first graph which is not a function. It has two points that lie on the __________ vertical line. You
can use this property as a _____________ test. It’s called the ___________ _________ test. If you can
___________ a vertical line anywhere on the graph with it only _____________ the vertical line at ________
place, the graph is a ______________.
Since we’re on the idea of functions, let’s continue on with them. Many ______________ can be represented
as an _____________ in two variable such as
. An ordered pair is a _____________ of such an
equation.
The ____________ of an equation is a ______________ of all points (x,y) whose ____________ are
_____________of the equation. That means, if you plug the x-coordinate in for x and the y-coordinate in for y
and evaluate, you will get a _______ statement.
We’re first going to graph _________ functions using a _________ of _________. A linear function has a graph
of a _______ and its __________ exponent is _______. A table of values is a table of ______ x- values that you
____________ to plug in to evaluate y so you can get an ordered pair to plot on the graph.
Examples
a)
b)
x y
x y
Anytime you have a function, you can ___________ it. When you name it, it will then be in ______________
notation. Look at the linear function a above. If we rename it f, we can then rewrite it in function notation to
make it look like
. That is read, “f of x is equal to x plus 1.” Paying attention to the “f of x”. It is
_____ multiplication or f times x, it is simply y but in function form. So instead of it being (x,y) for the ordered
pair, it will now look like (x, f(x)).
Keeping that in mind, let’s evaluate some functions. Decide whether the function is linear. Then evaluate the
function when
.
a)
b)