2.
- In Algebra I you learned about relations and functions.You will
recall that arelationis a set of ordered pairs, and afunctionis a
special relation that assigns each value in thedomain(the first
coordinate in the ordered pair, or the x value) to exactly one
value in therange(the second coordinate in the ordered pair, or the
y value).
Lets take aminute and do a more thorough review of these
concepts.Go now
tohttp://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=133
, login, and launch the GizmoIntroduction to Functions. Open the
Exploration Guide and follow the instructions. 3. Practice
- Try these problems on your own.Once you have answered a
problem, click once to see the answer.Remember to work each problem
first,thenclick to see the answer.
- Use a mapping diagram to determine if the relation is a
function
-
- (2, 7), (4, 1), (5, 9), (3, 2), (8, 0)
2 3 4 5 8 0 1 2 7 9 Since each value in the domain matches to
only one value in the range, the relation is a function. 4.
- Use a mapping diagram to determine if the relation is a
function.
- Use a mapping diagram to determine if the relation is a
function.
-
- (8, 1), (3, 4), (2, 7), (8, 5), (0, 6)
domain range 1 2 3 5 9 3 4 5 9 Since each value in the domain
matches to only one value in the range, the relation is a function.
domain range 0 2 3 8 1 4 5 6 7 Since a value in the domain (8)
matchesmore than onevalue in the range (1 and 5), the relationis
nota function. 2 5 3 1 9 5 9 4 4 3 5.
- 4.Use the vertical line test to determine if the relation is a
function.
Since a vertical line never touches more than one point at a
time, the relation is a function. 6. Evaluating functions
- Click on the link to see notes on evaluating functions.
- www.regentsprep.org/Regents/math/algtrig/ATP5/Evaluating
7. Practice Try these problems on your own.Once you have
answered a problem, click once to see the answer.Remember to work
each problem first,thenclick to see the answer. 3(7) 4 21 4 17 5 2+
2(5) + 1 25 + 10 + 1 36 f(x) = 3x 4 for x = 7 f(x) = x 2+ 2x + 1
for x = 5 8. Practice
- Find the range for the functionfor the domain
9. In Algebra 1 you learned the basics of domain and range.Click
on the link below to watch a video and refresh your memory on that
topic. Pearson Prentice Hall Mathematics Video 10. Many functions
can be represented by an equation in two variables.The input
variable is called the independent variable.The output variable in
an equation, which depends on the value of the input variable, is
called the dependent variable.Thedomainof a function consists of
the set of allinputvalues.Therangeof a function consist of the set
of alloutputvalues.A function is like a machine that you input
numbers and variables. The machine alters the input in some way and
produces an answer. 11. Example:Find the domain and range of the
following graph: What's thedomain ?The graph above is represented
by y = x 2 , and we can square any number we want.Therefore,
thedomainisall real numbers. On a graph the domain corresponds to
thehorizontal axis.Since that is the case, we need to look to the
left and right to see if there are any end points or holes in the
graph to help us find our domain. If the graph keeps going on and
on to the right and the graph keeps going on and on to the left
then the domain is represented by all real numbers. 12. What's
therange ?If I plug any number into this function, am I ever going
to be able to get a negative number out of it? No, not in the Real
Number System!Therangeof this function isall positive numberswhich
is represented byy 0. On a graph, the range corresponds to the
vertical axis. Since that is the case, we need to look up and down
to see if there are any end points or holes to help us find our
range. If the graph keeps going up and down with no endpoint then
the range is all real numbers.However, this is not the case.The
graph does not begin to touch the y-axis until x = 0, then it
continues up with no endpoints which is represented by y 0. 13.
Let's try another example: What numbers can we plug into this
function?What happens if we plug in 4? If x = 4, we divide by zero
which is undefined.Therefore, thedomainof this function is:all real
numbers except 4. Therangeisall real numbers except 0 . (We can
only produce zero when a zero is in the numerator.) , zero in the
numerator is OK! However,, zero in the denominator is a NO NO! In
general, when you're trying to find the domain of a function, there
are two things you should look out for.(1) Look for potential
division by zero.(2) Look for places where you might take the
square rootof a negative number.(3) If you have a verbal model, you
can only use numbers that make sense in the given situation.(This
is called the relevant domain as it only identifies the values that
make sense in the given situation.) 14. Practice Find the domain
and range a.{(2, 8), (5, 7), (6, 9), (3, 4)} b.
- Domain = all real numbers
15. Summary The domain of a function is all the possible input
values, and the range is all possible output values.
