Symmetry Answers
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Which of the following is an odd function?
A
f(x) = 3x2 + xB
f(x) = 4x3 + 7C
f(x) = 5x2 + 9D
f(x) = 6x3 + 2x2
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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).3
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).4
Which graph represents an even function?
A
On a coordinate plane, a hyperbola has a curve in quadrant 1 and a curve in quadrant 3. The curve in quadrant 1 has a vertex at (2, 2) and goes through points (1, 5) and (5, 1). The curve in quadrant 3 has a vertex at (negative 2, negative 2) and goes through points (negative 5, negative 1) and (negative 1, negative 5).
B
On a coordinate plane, a function has two curves. The first curve is asymptotic to x = negative 3, goes through (negative 2, 0), has a minimum of (negative 1.5, negative 1), goes through (negative 1, 0), and connects with the second curve at (0.5, 3). The second curve starts at (0.5, 3), goes through (2, 0), has a minimum of (2.5, negative 1), goes through (3, 0), and is asymptotic to x = 4.
C
On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (0, 4), and goes through (2, 0).
D
On a coordinate plane, a straight line has a negative slope. It goes through (negative 2, 4), crosses the y-axis at (0, 2), and crosses the x-axis at (2, 0).
5
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).
B
On a coordinate plane, a curved line crosses the x-axis at (negative 4, 0), (0, 0), and (4, 0).
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).
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).
7
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.8
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)9
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.10
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.
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).
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).
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).
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