Download Relations and Functions In this discussion, you will be assigned two

Relations and Functions
In this discussion, you will be assigned two equations with which you will then do a variety of
math work having to do with mathematical functions. Read the following instructions in order
and view the example to complete this discussion:

Find your two equations in the list below based on the last letter of your last name.
If the last letter of your last name
is
A or B
C or D
E or F
G or H
I or J
K or L
M or N
O or P
Q or R
S or T
U or V
W or X
Y or Z
On pages 708 – 711, solve the following
problems
22 and 30
24 and 32
26 and 34
28 and 36
12 and 46
14 and 48
16 and 50
18 and 52
20 and 54
2 and 56
4 and 58
6 and 60
8 and 64

There are many ways to go about solving math problems. For this assignment you will be
required to do some work that will not be included in the discussion. First, you need to
graph your functions so you can clearly describe the graphs in your discussion. Your
graph itself is not required in your post, although the discussion of the graph is required.
Make sure you have at least five points for each equation to graph. Show all math work
for finding the points.

Specifically mention any key points on the graphs, including intercepts, vertex, or
start/end points. (Points with decimal values need not be listed, as they might be found in
a square root function. Stick to integer value points.)

Discuss the general shape and location of each of your graphs.

State the domain and range for each of your equations. Write them in interval notation.

State whether each of the equations is a function or not giving your reasons for the
answer.

Select one of your graphs and assume it has been shifted three units upward and four
units to the left. Discuss how this transformation affects the equation by rewriting the
equation to incorporate those numbers.

Incorporate the following five math vocabulary words into your discussion. Use bold
font to emphasize the words in your writing (Do not write definitions for the words;
use them appropriately in sentences describing the thought behind your math
work.):
o Function
o Relation
o Domain
o Range
o Transformation
y = |x-1| +2
f(x) = |x-1| +2
x
1
2
−3
−2
−1
0
Domain = (−∞,∞)
f(x) = |x−1 |+2
2
3
4
3
2
3
Range = [2,∞)
f(x) = |x−1| +2
f(x) = |x−1| +2+3
f(x) = |x+4−1|+5
f(x) = |x+3|+5
x = −√y
f(y) = −√y
y
0
4
9
16
25
Domain = [0,−∞)
Range = [0,∞)
f(y)= −√y
0
−2
−3
−4
−5
The relation #20 from page pg. 708-711
The relation written with function notation.
This is the graph of the absolute value
function. From this graph I know that the
vertex is at (1, 2) and the V-shape opens
upward.
Because the V opens on both sides without
end, the domain is infinite in both directions.
Because the vertex is found at 2 on the y-axis
the graph cannot go any lower but it does
extend upward along the y-axis infinitely.
Now I will transform the above graph to
reflect a move of 3 units up and 4 units to the
left.
Adding 3 units up.
Adding 4 units to the left.
The relation is written to reflect the
transformation.
The relation #54 from pages 708-711.
The relation in function notation.
This is the graph of the square root function.
The y-coordinate was found first because in
this case x is not the independent variable. I
know from this graph that there can be no
negative values for y and therefore the graph
cannot cross the 0 point on the y-axis.
The line on this graph begins at (0,0) and
extends upward to the left infinitely.
Both of these relations are functions, I know this for two reasons. First, both relations pass the
vertical line test that is they do not touch any one vertical line more than once. The second way I
have determined they are both functions is that the value for x is not repeated in either case.