Answers2627 ALGEBRA II AFunction Operations

Symmetry Answers

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If f(x) = (xm + 9)2, which statement about f(x) is true?

A
f(x) is an even function for all values of m.
B
f(x) is an even function for all even values of m.
C
f(x) is an odd function for all values of m.
D
f(x) is an odd function for all odd values of m.
2
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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
3

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
4

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)
5

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.
6

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
7

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.
8

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).
9

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.
10

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

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