Answers LAUSD-Algebra II A Prescriptive - SummerRelations and Functions

Symmetry Answers

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Which of the following is an even function?

f(x) = |x|

f(x) = x3 – 1

f(x) = –3x

f (x) = RootIndex 3 StartRoot x EndRoot

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Which of the following is an odd function?

f(x) = 3x2 + x

f(x) = 4x3 + 7

f(x) = 5x2 + 9

f(x) = 6x3 + 2x

Which statement best describes how to determine whether f(x) = x4 – x3 is an even function?

Determine whether (–x)4 – (–x)3 is equivalent to x4 – x3.

Determine whether (–x4) – (–x3) is equivalent to x4 + x3.

Determine whether (–x)4 – (–x)3 is equivalent to –(x4 – x3).

Determine whether (–x4) – (–x3) is equivalent to –(x4 + x3).

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

f(x) can be odd or even.

f(x) can be odd but cannot be even.

f(x) can be even but cannot be odd.

f(x) cannot be odd or even.

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

It has rotational symmetry about the origin.

It has line symmetry about the line y = x.

It has line symmetry about the y-axis.

It has line symmetry about the x-axis.

Which graph represents an odd function?

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).

On a coordinate plane, a curved line crosses the x-axis at (negative 4, 0), (0, 0), and (4, 0).

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).

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).

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?

one

two

six

eight

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?

It includes points in Quadrant I.

It includes points in Quadrant II.

It does not include points in Quadrant I.

It does not include points in Quadrant II.

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)?

(–6, 0), (–2, 0), and (0, 0)

(–6, 0), (–2, 0), and (4, 0)

(–4, 0), (0, 0), and (2, 0)

(–4, 0), (–2, 0), and (0, 0)

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

Determine whether 9 – 4(–x)2 is equivalent to 9 – 4x2.

Determine whether 9 – 4(–x2) is equivalent to 9 + 4x2.

Determine whether 9 – 4(–x)2 is equivalent to –(9 – 4x2).

Determine whether 9 – 4(–x2) is equivalent to –(9 + 4x2).

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