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Math Problems
Algebra 2
Even and odd functions
Is the function
s
(
x
)
=
5
x
7
+
2
x
3
−
9
x
s(x) = 5x^7 + 2x^3 - 9x
s
(
x
)
=
5
x
7
+
2
x
3
−
9
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
n
(
x
)
=
−
5
x
3
−
x
2
n(x) = -5x^3 - x^2
n
(
x
)
=
−
5
x
3
−
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
p
(
x
)
=
2
x
4
−
3
x
2
+
6
p(x) = 2x^4 - 3x^2 + 6
p
(
x
)
=
2
x
4
−
3
x
2
+
6
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
b
(
x
)
=
−
2
x
2
+
6
b(x) = -2x^2 + 6
b
(
x
)
=
−
2
x
2
+
6
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
t
(
x
)
=
4
x
6
+
13
t(x) = 4x^6 + 13
t
(
x
)
=
4
x
6
+
13
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
d
(
x
)
=
x
4
−
x
2
d(x) = x^4 - x^2
d
(
x
)
=
x
4
−
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
h
(
x
)
=
3
x
5
+
2
x
3
−
4
x
2
h(x) = 3x^5 + 2x^3 - 4x^2
h
(
x
)
=
3
x
5
+
2
x
3
−
4
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
j
(
x
)
=
11
x
2
−
18
j(x) = 11x^2 - 18
j
(
x
)
=
11
x
2
−
18
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
m
(
x
)
=
−
4
x
5
+
6
x
m(x) = -4x^5 + 6x
m
(
x
)
=
−
4
x
5
+
6
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
p
(
x
)
=
5
x
3
−
2
x
+
11
p(x) = 5x^3 - 2x + 11
p
(
x
)
=
5
x
3
−
2
x
+
11
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
h
(
x
)
=
x
3
+
2
x
h(x) = x^3 + 2x
h
(
x
)
=
x
3
+
2
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
r
(
x
)
=
3
x
6
+
x
2
r(x) = 3x^6 + x^2
r
(
x
)
=
3
x
6
+
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
b
(
x
)
=
3
x
3
−
x
b(x) = 3x^3 - x
b
(
x
)
=
3
x
3
−
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
w
(
x
)
=
−
2
x
5
+
7
x
2
w(x) = -2x^5 + 7x^2
w
(
x
)
=
−
2
x
5
+
7
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
k
(
x
)
=
−
4
x
6
+
11
x
k(x) = -4x^6 + 11x
k
(
x
)
=
−
4
x
6
+
11
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
w
(
x
)
=
3
x
7
+
9
x
3
w(x) = 3x^7 + 9x^3
w
(
x
)
=
3
x
7
+
9
x
3
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
k
(
x
)
=
−
5
x
7
−
2
x
3
+
x
k(x) = -5x^7 - 2x^3 + x
k
(
x
)
=
−
5
x
7
−
2
x
3
+
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
q
(
x
)
=
−
4
x
4
−
3
x
3
q(x) = -4x^4 - 3x^3
q
(
x
)
=
−
4
x
4
−
3
x
3
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
r
(
x
)
=
2
x
4
−
6
x
2
+
8
x
r(x) = 2x^4 - 6x^2 + 8x
r
(
x
)
=
2
x
4
−
6
x
2
+
8
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
g
(
x
)
=
2
x
7
−
x
5
−
6
x
3
g(x) = 2x^7 - x^5 - 6x^3
g
(
x
)
=
2
x
7
−
x
5
−
6
x
3
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
q
(
x
)
=
x
6
−
9
q(x) = x^6 - 9
q
(
x
)
=
x
6
−
9
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
g
(
x
)
=
2
x
8
−
x
6
+
7
g(x) = 2x^8 - x^6 + 7
g
(
x
)
=
2
x
8
−
x
6
+
7
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
v
(
x
)
=
−
x
7
+
8
x
5
v(x) = -x^7 + 8x^5
v
(
x
)
=
−
x
7
+
8
x
5
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
s
(
x
)
=
−
x
4
+
8
x
3
−
9
x
2
s(x) = -x^4 + 8x^3 - 9x^2
s
(
x
)
=
−
x
4
+
8
x
3
−
9
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
v
(
x
)
=
−
x
6
+
4
x
2
−
1
v(x) = -x^6 + 4x^2 - 1
v
(
x
)
=
−
x
6
+
4
x
2
−
1
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
h
(
x
)
=
−
3
x
8
+
x
4
−
2
x
2
h(x) = -3x^8 + x^4 - 2x^2
h
(
x
)
=
−
3
x
8
+
x
4
−
2
x
2
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
v
(
x
)
=
x
5
−
4
x
4
v(x) = x^5 - 4x^4
v
(
x
)
=
x
5
−
4
x
4
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
n
(
x
)
=
2
x
5
+
x
3
n(x) = 2x^5 + x^3
n
(
x
)
=
2
x
5
+
x
3
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
n
(
x
)
=
−
x
4
+
3
x
2
−
4
n(x) = -x^4 + 3x^2 - 4
n
(
x
)
=
−
x
4
+
3
x
2
−
4
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Is the function
t
(
x
)
=
−
4
x
7
+
2
x
t(x) = -4x^7 + 2x
t
(
x
)
=
−
4
x
7
+
2
x
even, odd, or neither?
\newline
Choices:
\newline
(A)even
\newline
(B)odd
\newline
(C)neither
Get tutor help
Tamara was asked to determine whether
f
(
x
)
=
x
4
−
2
x
2
f(x)=x^{4}-2 x^{2}
f
(
x
)
=
x
4
−
2
x
2
is even, odd, or neither. Here is her work:
\newline
Step
1
1
1
: Find expression for
f
(
−
x
)
f(-x)
f
(
−
x
)
\newline
f
(
−
x
)
=
(
−
x
)
4
−
2
(
−
x
)
2
=
x
4
−
2
x
2
\begin{aligned} f(-x) & =(-x)^{4}-2(-x)^{2} \\ & =x^{4}-2 x^{2} \end{aligned}
f
(
−
x
)
=
(
−
x
)
4
−
2
(
−
x
)
2
=
x
4
−
2
x
2
\newline
Step
2
2
2
: Check if
f
(
−
x
)
f(-x)
f
(
−
x
)
is equal to
f
(
x
)
f(x)
f
(
x
)
or
−
f
(
x
)
-f(x)
−
f
(
x
)
\newline
x
4
−
2
x
2
x^{4}-2 x^{2}
x
4
−
2
x
2
is the same as
\newline
f
(
x
)
=
x
4
−
2
x
2
.
f(x)=x^{4}-2 x^{2} \text {. }
f
(
x
)
=
x
4
−
2
x
2
.
\newline
Step
3
3
3
: Conclusion
\newline
f
(
−
x
)
f(-x)
f
(
−
x
)
is equivalent to
f
(
x
)
f(x)
f
(
x
)
, so
f
f
f
is even.
\newline
Is Tamara's work correct? If not, what is the first step where Tamara made a mistake?
\newline
Choose
1
1
1
answer:
\newline
(A) Tamara's work is correct.
\newline
(B) Tamara's work is incorrect. She first made a mistake in Step
1
1
1
.
\newline
(C) Tamara's work is incorrect. She first made a mistake in Step
2
2
2
.
\newline
(D) Tamara's work is incorrect. She first made a mistake in Step
3
3
3
.
Get tutor help
Determine whether the lines are parallel, perpendicular or neither.
\newline
y
=
3
4
x
+
2
8
x
+
6
y
=
12
\begin{array}{l} y=\frac{3}{4} x+2 \\ 8 x+6 y=12 \end{array}
y
=
4
3
x
+
2
8
x
+
6
y
=
12
\newline
Parallel
\newline
perpendicular
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
−
6
x
−
1
f(x)=-6 x-1
f
(
x
)
=
−
6
x
−
1
is even, odd or neither.
\newline
even
\newline
odd
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
8
x
4
+
x
2
+
x
6
f(x)=8 x^{4}+x^{2}+x^{6}
f
(
x
)
=
8
x
4
+
x
2
+
x
6
is even, odd or neither.
\newline
odd
\newline
even
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
−
2
x
4
+
x
5
f(x)=-2 x^{4}+x^{5}
f
(
x
)
=
−
2
x
4
+
x
5
is even, odd or neither.
\newline
odd
\newline
even
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
−
x
3
+
x
5
f(x)=-x^{3}+x^{5}
f
(
x
)
=
−
x
3
+
x
5
is even, odd or neither.
\newline
even
\newline
odd
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
−
9
x
2
+
1
−
x
3
f(x)=-9 x^{2}+1-x^{3}
f
(
x
)
=
−
9
x
2
+
1
−
x
3
is even, odd or neither.
\newline
even
\newline
odd
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
8
x
7
−
3
x
5
+
3
x
f(x)=8 x^{7}-3 x^{5}+3 x
f
(
x
)
=
8
x
7
−
3
x
5
+
3
x
is even, odd or neither.
\newline
even
\newline
neither
\newline
odd
Get tutor help
Determine whether the function
f
(
x
)
=
−
7
x
3
+
x
5
f(x)=-7 x^{3}+x^{5}
f
(
x
)
=
−
7
x
3
+
x
5
is even, odd or neither.
\newline
neither
\newline
odd
\newline
even
Get tutor help
Determine whether the function
f
(
x
)
=
x
6
+
7
x
2
−
1
f(x)=x^{6}+7 x^{2}-1
f
(
x
)
=
x
6
+
7
x
2
−
1
is even, odd or neither.
\newline
odd
\newline
neither
\newline
even
Get tutor help
Determine whether the function
f
(
x
)
=
3
x
−
7
x
5
+
2
x
2
f(x)=3 x-7 x^{5}+2 x^{2}
f
(
x
)
=
3
x
−
7
x
5
+
2
x
2
is even, odd or neither.
\newline
odd
\newline
neither
\newline
even
Get tutor help
Determine whether the function
f
(
x
)
=
1
−
x
4
+
6
x
6
f(x)=1-x^{4}+6 x^{6}
f
(
x
)
=
1
−
x
4
+
6
x
6
is even, odd or neither.
\newline
odd
\newline
even
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
−
8
x
3
−
7
x
4
f(x)=-8 x^{3}-7 x^{4}
f
(
x
)
=
−
8
x
3
−
7
x
4
is even, odd or neither.
\newline
neither
\newline
even
\newline
odd
Get tutor help
Determine whether the function
f
(
x
)
=
−
7
x
3
−
x
4
f(x)=-7 x^{3}-x^{4}
f
(
x
)
=
−
7
x
3
−
x
4
is even, odd or neither.
\newline
even
\newline
odd
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
x
4
+
5
x
6
−
6
f(x)=x^{4}+5 x^{6}-6
f
(
x
)
=
x
4
+
5
x
6
−
6
is even, odd or neither.
\newline
even
\newline
neither
\newline
odd
Get tutor help
Determine whether the function
f
(
x
)
=
x
5
−
3
f(x)=x^{5}-3
f
(
x
)
=
x
5
−
3
is even, odd or neither.
\newline
neither
\newline
even
\newline
odd
Get tutor help
Determine whether the function
f
(
x
)
=
6
x
5
−
x
2
f(x)=6 x^{5}-x^{2}
f
(
x
)
=
6
x
5
−
x
2
is even, odd or neither.
\newline
even
\newline
neither
\newline
odd
Get tutor help
Determine whether the function
f
(
x
)
=
−
6
x
6
+
1
+
x
4
f(x)=-6 x^{6}+1+x^{4}
f
(
x
)
=
−
6
x
6
+
1
+
x
4
is even, odd or neither.
\newline
even
\newline
odd
\newline
neither
Get tutor help
Determine whether the function
f
(
x
)
=
−
3
−
x
4
+
7
x
f(x)=-3-x^{4}+7 x
f
(
x
)
=
−
3
−
x
4
+
7
x
is even, odd or neither.
\newline
odd
\newline
neither
\newline
even
Get tutor help
Determine whether the function
f
(
x
)
=
−
x
7
−
x
+
x
3
f(x)=-x^{7}-x+x^{3}
f
(
x
)
=
−
x
7
−
x
+
x
3
is even, odd or neither.
\newline
neither
\newline
even
\newline
odd
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