Download Graphing Test Review Answers

Graphing Test Review Answers
1. A relation is a set of ordered pairs
2. A function is a special relation in which each domain is paired with exactly one range.
 Every x only has 1 y
 x doesn’t repeat
 Remember the boyfriend/girlfriend analogy we used in class
3. (5 Rules)
1. no more than 2 variables
2. no other power than 1
3. no variable inside absolute value
4. no product of variables
5. no variable in the denominator
4. An x-intercept is where a graph crosses the x-axis. It occurs when y = 0 (because on the x-axis, y is always
0.)
5. A y-intercept is where a graph crosses the y-axis. It occurs when x = 0 (because on the y-axis, x is always
0.)
6. Slope describes how steep a line is and which way the line is going. Other words for slope include rate, rate
rise
of change,
, m.
run
7. To find slope use m 
rise
y  y2
or m  1
run
x1  x2
8. The slope-intercept form of a line is y = mx + b, where x and y are ordered pairs on that line, m is the slope,
and b is the y-intercept.
9. The graph of y = 6 is a horizontal line. The slope of a horizontal line is 0.
10. The graph of x = 4 is a vertical line. The slope of a vertical line is undefined.
11. A line that has a positive slope is always rising.
12. A line that has a negative slope is always falling.
13. To see whether or not a graph is a function use the Vertical Line Test. If you can draw a vertical line
through a graph and the line hits the graph more than once, then the graph is NOT a function.
14. Function: yes (because x doesn’t repeat)
Inverse: {(1, 2), (4, 0), (1, –1), (3, –2)}
The inverse is not a function (1 repeats for x).
15. Function: No (1 repeats for x)
Inverse: {(2, 1), (–4, 9), (4, 1), (–3, –3)}
The inverse is a function (x doesn’t repeat).
16. Not a function (use Vertical Line Test and the graph hits the line twice).
17. Yes, the graph is a function (use VLT).
18. (hint: you are given domain (x), so plug {–4, 0, 3} in for x. You could also make a table in your calculator
by going to y =, typing in your function, and hitting 2nd, Graph. In your table you are looking for when x is –4,
0, and 3n)
Range: {–18, –6, 3}
19. (hint: you are given range (y), so plug in {–2, 6, 10} in for g(x), which remember is just a fancy nickname
for y. Solve for x. Also, you can make a table in your calculator by going to y =, typing in your function, and
hitting 2nd, Graph. In your table, you are looking for when y is –2, 6, and 10.)
Domain: {–3, 1, 3}
20. (hint: To find domain, ask yourself “how far does the graph go left, and how far does the graph go right?”
Then to find range, ask yourself “how far down does the graph go, and how far up does the graph go?”
Domain: All Real Numbers
Range: y ≥ –2 (The graph goes UP from –2)
21. Yes, it is linear because it passes the 5 Rules.
Slope intercept form (get y by itself by getting rid of
m=
9
2
1
9
…multiply by the reciprocal): y  12  x
3
2
b = 12
22. Yes, it is linear because it passes the 5 Rules.
1
1
, subtract the x from both sides, then divide
6
3
1
2
both sides by
[or multiply by the reciprocal, which is –2]): y  14  x
2
3
2
m=
b = 14
3
Slope intercept form (get y by itself…distribute the
23. No, it is not linear because you cannot multiply variables together.
24. (hint: If an ordered pair is on a line, then you should be able to plug it in to x and y and it give you a true
statement. To find other ordered pairs, plug in any random number for x and solve for y OR use your calculator
by going to y =, typing in your equation, and making a table by going to 2nd, graph).
The point (3, 1) does lie on the line because when you plug in the point into the equation, you get a true
statement (1 = 1).
25. (hint: To find the x-intercept, substitute 0 in for y. To find the y-intercept, either let x = 0 OR get the
equation into slope intercept form.)
12
x-intercept: (  , 0)
y-intercept: (0, 4)
5
26. There is no x-intercept because this graph is a horizontal line, and if you think about the graph of a
horizontal line, it will never cross the x-axis. Also, there is no x in the problem to solve for.
x-intercept: none
y-intercept: (0, 6)
27. x-intercept: (–1, 0)
y-intercept: (0,
28. (hint: to find the slope use the formula m 
count the slope using
Slope =
1
5
2
)
5
y1  y2
OR graph the points given on a coordinate plane and
x1  x2
rise
)
run
29. Slope = 3 (Be sure to always reduce your slope as much as possible)
30. (hint: to find the slope of the graph, find two points that are on the graph and count using
Slope =
rise
)
run
2
3
31. (hint: to graph, get the equation into slope-intercept form (y by itself), use your y-intercept, then your
slope…OR find 2 points on the line by plugging in numbers for x and solving for y…OR find the intercepts and
plot them)
y = –2x – 2
●
●
32. y 
1
x2
2
●
●
33. (hint: to write the equation, use your slope and the point and plug into y = mx + b to find your y-intercept.)
y = –5x + 6
34. (hint: use your two points to find your slope using m 
y1  y2
, then plug in your slope and one of the
x1  x2
points into y = mx + b to find your y-intercept.
5
33
y  x
4
4
35. (hint: same process as #34…to check your answer you could always plug your answer into y = in the
calculator, type in your equation, and make a table by hitting 2nd, graph. See if you table matches theirs.)
y = –2x + 0 OR
y = –2x
36. (hint: find your equation by using the same process as in #34 and #35. Then, plug in 28 for x into your
equation OR type in the equation you got into y = in your calculator, make a table, and see what y is when x is
28.)
Equation to use: y = 3x
Answer: y is 84 when x is 28
37. (hint: parallel means same slope. Find the slope of their line by getting y by itself (slope-intercept form).
Then, use the same slope and the point given into y = mx + b to find your new y-intercept.)
5
y  x9
3
38. (hint: perpendicular means opposite reciprocal slopes (flip AND change sign of their slope). Find the
slope of their line by getting y by itself, flip their slope and change its sign, use that slope and the point given
into y = mx + b and find b.)
2
y  x  12
3
39. (hint: to graph 2x – y < 4, get y by itself, graph b and use slope, graph a BROKEN line, and shade…BE
SURE TO FLIP THE INEQUALITY SIGN WHEN YOU DIVIDE BY A NEGATIVE!!!)
y > 2x – 4
Other points are
Anything in the shaded region
●
●
40. (hint: find where your graph crosses the y-axis, then count to find your slope. The line is BROKEN and
shaded UP, so use > sign.)
y > 2x + 2
41. (hint: plug in the points. The ordered pair that gives you a true statement is the solution. OR graph it in
your calculator and see which ordered pair is in the shaded region. Remember, to get rid of the decimals on
your ordered pairs hit ZOOM, Integer and hit Enter at the origin.)
A, C, D