test review symmetery etc
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School
Clayton High, Clayton *
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Course
174
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
7
Uploaded by 25falsafielisa
Even/odd functions worksheet
Name:______________________________
Mixture of multiple choice and completion...
1.
Which function is an even function?
a. y = h(x) =
√
b.
y = p(x) = x
3
c.
y = R(x) =
d.
y =
|x|
2. Which function graphed below has exactly 3 real zeros?
3.
Which function is an odd function but the origin is not included as a point
on the graph of the function?
a. y = h(x) =
√
b.
y = p(x) = x
3
c.
y = R(x) =
d.
y =
|x|
4. You
want to move the graph of
b(x) = 2
√
+ 6
down 10 units. What will be the equation for your new
graph?
a.
y = 2
√
- 4
b.
y = -10
√
+6
c. y = -2
√
+ 6
d. .
y = 2
√
-
10
5.
Examine these functions. Which statement is correct?
a.
Graph I
is the graph of an even function.
c. Graph III is symmetric to the y-axis.
b. Graph II is symmetric to the x-axis.
d.
Graph IV is an odd function.
6. Which function could be an even function?
a) A function known as d(x)
where d(3) = 10 and d (-3) = -10
b) A function known as k(x)
where k(7) = 20 and
k(-7) = 20
c) A function known as M(x)
where M(4) = 10 and M (-4) =
0
d) A function known as C(x)
where C(7) = - 6 and C(-7) = 6
7.
Start with the incomplete graph of
p(x) as shown. Complete the graph if p(x) is symmetric to the origin.
.
8. Start with the incomplete graph of
f(x) as shown. Complete the graph if f(x) is symmetric to the y-axis.
9.
Start with the complete graph of
g(x) as shown. Graph - g(x) on the blank grid.
10. Avanti wants to understand why some equations have 2 solutions that are opposites.
10
9
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9 10
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9
10
He knows that the following equations have two solutions that are opposites:
Quadratic without an x term:
If
x
2
= 4 then x =
√
2 or x = -
√
- 2.
{ -2, 2 }
Basic Absolute Value:
If |x| = 4 then x = 4 or x = -4.
{ -4 , 4 }
The reason these equations have 2 solutions that are opposites
can best be explained by the fact that:
a. The graphs of
f(x) = x
2
and
g(x) = |x| are symmetric to the origin.
b. The graphs of
f(x) = x
2
and
g(x) = |x| are symmetric to the x-axis.
c.
The graphs of
f(x) = x
2
and
g(x) = |x| are symmetric to the y-axis.
d.
All equations have 2 solutions.
11. If
g(x) is an odd function and g(5) = -7, which one of the following must be true?
a.
g(-5) = 7
b.
g(-5) = -7
c.
g(-7) = 5
d. g(7) = - 5
12.
Which quadratic function is the correct graph of the function Q(x)?
y =Q(x) = -1(x
–
4)(x +2)
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13. The graph of y= f(x) is shown. Sketch the graph of y =
|
f(x)
|
on the blank grid below.
14.
Analyze the graph of F(x) as shown. Which statement is
not correct?
a. The roots of the function are at approximately
x = 0, x = 2.2 , and x = 6.8
b. The function is increasing on the interval
1 <
x <
5
c. There is a relative maximum of y = 7 when x = 1
d.
The domain of the function is ( -
∞
,
∞)
15.
Match the given equations with the correct graph.
y = j(x) =
√
3
y = c(x) =
x
3
+ 4
y=h(x) = -3 x + 6
y = g(x) =
| |
y = n(x) =
y = w(x) = -2 x
2
–
5
16. Solve each of the following for x:
a.
2x = 16
_______________
b.
2 x
2
= 16
__________________
c.
2 x
3
= 16 ______________
d.
2 |x| = 16 _____________
e.
2
√
= 16
_________________
f.
= 16
______________
17. Refer to #16.
a. Which equation is quadratic?______________
b. linear?___________
c.
radical?____________
d. rational? _______________
e. cubic? _______________
18. Where do the graphs of y=f(x) = 3x +8
and h(x) = -x +20
intersect?
Use ( x, y) form for your answer.
a.
(2, 14)
b.
(2, 6)
c.
(3, 17)
d.
( -3, 23)
19.
If 2
√
+ 18 = 12
then
2
√
= -6
then
√
= -3 then square it to yield x = 9.
Is this correct?
a. yes, it checks
b. yes but also include -9 due to the fact that y =
√
is an even function
c. no, x = -9
d. no, sq.root cannot be negative so x =9 is extraneous, thus no solution.
20.
Manuel wants to solve
x
2
= 2x + 8
by using geometry. He graphs y = x
2
and y = 2x + 8 as shown.
Use the graph
to solve this quadratic equation. Check your answers in a calculator or by using algebra (zero product property).
Answer(s): ________________________________
21.
f(x) = -3x
2
+ 6 then which statement is not correct?
a. The zeros of the function are x =
√
or x = -
√
b. The range is
[6,
∞
)
c.
The vertical intercept, or y-intercept, is at (0, 6).
D.
f(- x) = f(x)
22.
A table for y =x
2
- 3x - 10
is shown. Use the table to solve x
2
- 3x - 10 = 0
for x.
23.
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24.
Describe the transformation from the parent graph. Make a quick sketch.
a.
y =
x
2
+
6
_______________________________________________
b.
y = -7 + |x|
______________________________________________
c.
y = 2 + 5
x
3
__________________________________________________
d.
y =
- 10
__________________________________
e.
y =
√
_____________________________________
f.
y =
√
_____________________________________
g.
y =
- x
2
+ 4
_________________________________________________
h.
y =
- 3
__________________________________
25. Which function is odd (symmetric to the origin)?
a.
y = -3x
3
+ 5
b.
y = - 4 x +2
c.
y = x
2
+ 4
d.
y = - 4x
3
26. Which function is not even (symmetric to the y-axis)?
a. y = -4 x
2
+ 3
b.
y = 2
|x|
- 6
c.
y = x
2
+6x +5
d.
y = 6