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Symmetry Answers

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The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function, what is the greatest number of points that can lie in Quadrant II?

A
one
B
two
C
six
D
eight
2
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Which statement best describes how to determine whether f(x) = x4 – x3 is an even function?

A
Determine whether (–x)4 – (–x)3 is equivalent to x4 – x3.
B
Determine whether (–x4) – (–x3) is equivalent to x4 + x3.
C
Determine whether (–x)4 – (–x)3 is equivalent to –(x4 – x3).
D
Determine whether (–x4) – (–x3) is equivalent to –(x4 + x3).
3

Which of the following is an odd function?

A
f(x) = 3x2 + x
B
f(x) = 4x3 + 7
C
f(x) = 5x2 + 9
D
f(x) = 6x3 + 2x
4

If f(x) is an even function, which statement about the graph of f(x) must be true?

A
It has rotational symmetry about the origin.
B
It has line symmetry about the line y = x.
C
It has line symmetry about the y-axis.
D
It has line symmetry about the x-axis.
5

The graph of the even function f(x) has five x-intercepts. If (6, 0) is one of the intercepts, which set of points can be the other x-intercepts of the graph of f(x)?

A
(–6, 0), (–2, 0), and (0, 0)
B
(–6, 0), (–2, 0), and (4, 0)
C
(–4, 0), (0, 0), and (2, 0)
D
(–4, 0), (–2, 0), and (0, 0)
7

Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?

A
f(x) can be odd or even.
B
f(x) can be odd but cannot be even.
C
f(x) can be even but cannot be odd.
D
f(x) cannot be odd or even.
8

Which phrase best describes f(x), graphed on the coordinate plane below?

Question illustration
A
f(x) is an odd function.
B
f(x) is an even function.
C
f(x) is both odd and even.
D
f(x) is neither odd nor even.
9

Which graph represents an odd function?

A
On a coordinate plane, a function has two curves. The first curve is in quadrants 2 and 3 and has a minimum value of (negative 1, negative 3). The curve intersects the x-axis at (negative 2, 0) and goes to (0, 0). The second curve is in quadrants 1 and 4 and has a minimum value of (1, negative 3). The curve starts at (0, 0) and intercepts the x-axis at (2, 0).
Option A
B
On a coordinate plane, a curved line crosses the x-axis at (negative 4, 0), (0, 0), and (4, 0).
Option B
C
On a coordinate plane, a v-shaped function opens up. The function goes through (0, 2), has a vertex at (2, 0), and goes through (5, 3).
Option C
D
On a coordinate plane, a curve has a maximum point at (0.5, 1) and a minimum point at (2, 0). The curve goes through points (0, 0) and (3, 4).
Option D
10

Which graph shows rotational symmetry?

A
On a coordinate plane, a sine curve goes through one cycle and is represented by f (x). The curve has a minimum of (2, negative 2), a maximum of (negative 2, 2), and goes through (0, 0).
Option A
B
On a coordinate plane, the function g(x) has two connected curves. The first curve goes through point (negative 3, negative 2) to (0, 0). The second curve goes from (0, 0) through (2, 3).
Option B
C
On a coordinate plane, the function h (x) is a v shape that opens down. The function has a vertex at (0,0) and goes through (negative 4, negative 4) and (4, negative 4).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).
Option D
11

Which graph shows line symmetry about the y-axis?

A
On a coordinate plane, a curve is asymptotic to the x-axis and y-axis in quadrant 4.
Option A
B
On a coordinate plane, a curve goes through one and one-half cycles. For the first curve, the maximum is at (negative 3, 1) and the minimum is (0, negative 1). For the half curve, the maximum is at (3, 1).
Option B
C
On a coordinate plane, two straight lines connect at (0, 0). The first line has a negative slope and goes through (negative 1, 3). The second line has a negative slope and goes through (3, negative 1).
Option C
D
On a coordinate plane, a curve has a minimum point at (negative 2.5, negative 5) and a maximum point at (2.5, 5).
Option D
12

Which statement best describes how to determine whether f(x) = 9 – 4x2 is an odd function?

A
Determine whether 9 – 4(–x)2 is equivalent to 9 – 4x2.
B
Determine whether 9 – 4(–x2) is equivalent to 9 + 4x2.
C
Determine whether 9 – 4(–x)2 is equivalent to –(9 – 4x2).
D
Determine whether 9 – 4(–x2) is equivalent to –(9 + 4x2).
13

If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, which statement about the graph of f(x) must be true?

A
It includes points in Quadrant I.
B
It includes points in Quadrant II.
C
It does not include points in Quadrant I.
D
It does not include points in Quadrant II.
14

Which of the following is an even function?

A
f(x) = |x|
B
f(x) = x3 – 1
C
f(x) = –3x
D
f (x) = RootIndex 3 StartRoot x EndRoot
Option D
15

Which statement best describes how to determine whether f(x) = x3 + 5x + 1 is an even function?

A
Determine whether –(x3 + 5x + 1) is equivalent to x3 + 5x + 1.
B
Determine whether (–x)3 + 5(–x) + 1 is equivalent to x3 + 5x + 1.
C
Determine whether –x3 + 5x + 1 is equivalent to –(x3 + 5x + 1).
D
Determine whether (–x)3 + 5(–x) + 1 is equivalent to –(x3 + 5x + 1).
16

Which of the following is an even function?

A
f(x) = (x – 1)2
B
f(x) = 8x
C
f(x) = x2 – x
D
f(x) = 7

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