Symmetry Answers
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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.3
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).
4
Which of the following is an even function?
A
f(x) = (x – 1)2B
f(x) = 8xC
f(x) = x2 – xD
f(x) = 75
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).6
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).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 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).
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
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).Did you find these answers helpful?
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