Symmetry Answers
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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.2
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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).
3
Which of the following is an even function?
A
f(x) = (x – 1)2B
f(x) = 8xC
f(x) = x2 – xD
f(x) = 74
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
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).6
Which phrase best describes f(x), graphed on the coordinate plane below?
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.7
Which of the following is an even function?
A
f(x) = |x|B
f(x) = x3 – 1C
f(x) = –3xD
f (x) = RootIndex 3 StartRoot x EndRoot
8
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.9
Which of the following is an odd function?
A
f(x) = 3x2 + xB
f(x) = 4x3 + 7C
f(x) = 5x2 + 9D
f(x) = 6x3 + 2x10
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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