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Symmetry — Quiz Answers

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The graph of the even function f of x has five x -intercepts. If open paren 6 comma 0 close paren is one of the intercepts, which set of points can be the other x -intercepts of the graph of f of x ?

A
open paren negative 4 comma 0 close paren , open paren 0 comma 0 close paren , and open paren 2 comma 0 close paren
B
open paren negative 6 comma 0 close paren , open paren negative 2 comma 0 close paren , and open paren 0 comma 0 close paren
C
open paren negative 4 comma 0 close paren , open paren negative 2 comma 0 close paren , and open paren 0 comma 0 close paren
D
open paren negative 6 comma 0 close paren , open paren negative 2 comma 0 close paren , and open paren 4 comma 0 close paren
2
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The graph of f of x consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f of x is an odd function, what is the greatest number of points that can lie in Quadrant II?

A
eight
B
six
C
one
D
four
3

Which statement best describes how to determine whether f of x is equal to x cubed plus 5 x plus 1 is an even function?

A
Determine whether negative x cubed plus 5 x plus 1 is equivalent to negative open paren x cubed plus 5 x plus 1 close paren .
B
Determine whether negative x cubed plus 5 times negative x plus 1 is equivalent to x cubed plus 5 x plus 1 .
C
Determine whether negative open paren x cubed plus 5 x plus 1 close paren is equivalent to x cubed plus 5 x plus 1 .
D
Determine whether negative x cubed plus 5 times negative x plus 1 is equivalent to negative open paren x cubed plus 5 x plus 1 close paren .
4

Which graph shows line symmetry about the y -axis?

A
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve k of x with three x-intercepts at (negative 4 comma 0), (0 comma 0), and (4 comma 0). The curve starts in the second quadrant, goes down to the third quadrant, moves up and goes to the first quadrant, and finally goes to the fourth quadrant.
B
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1.The graph has a curve f of x in the fourth quadrant which is asymptotic to the x-axis and y-axis.
C
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a v-shaped curve h of x that has a vertex at (0 comma 0). The left side line has a negative slope and goes through (negative 1 comma 3). The right side line has a negative slope and goes through (3 comma negative 1).
D
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve g of x with crests and troughs. The crests are at (negative 3 comma 1), and (3 comma 1), and trough at (0 comma negative 1). The curve has 4 x-intercepts.
5

Which graph shows rotational symmetry?

A
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve g of x split into two small curves so that one curve is the mirror image of the other. The first curve goes through the points (negative 3 comma negative 2) and (0 comma 0). The second curve goes through (0 comma 0) and (2 comma 3).
B
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph is a v-shaped curve h of x that opens downwards with vertex at (0 comma 0). The curve goes through (negative 4 comma negative 4) and (4 comma negative 4).
C
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a parabola k of x opens upwards with vertex at (0 comma 0). It goes through (negative 2 comma 4) and (2 comma 4).
D
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve f of x with crests and troughs and passes through the origin. The crest is at (negative 2 comma 2), and the trough is at (2 comma negative 2). The curve has 3 x-intercepts.
6

Which statement best describes how to determine whether f of x is equal to 9 minus 4 x squared is an odd function?

A
Determine whether 9 minus 4 times negative x squared is equivalent to 9 minus 4 x squared .
B
Determine whether 9 minus 4 times negative x squared is equivalent to negative open paren 9 minus 4 x squared close paren .
C
Determine whether 9 minus 4 times open paren negative x squared close paren is equivalent to negative open paren 9 plus 4 x squared close paren .
D
Determine whether 9 minus 4 times open paren negative x squared close paren is equivalent to 9 plus 4 x squared .
7

If f of x is an odd function and the graph of f of x includes points in Quadrant IV, which statement about the graph of f of x must be true?

A
It does not include points in Quadrant II.
B
It includes points in Quadrant I.
C
It does not include points in Quadrant I.
D
It includes points in Quadrant II.
8

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

A
It has line symmetry about the x -axis.
B
It has line symmetry about the line y is equal to x .
C
It has line symmetry about the y -axis.
D
It has rotational symmetry about the origin.
9

Which graph represents an odd function?

A
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a W-shaped curve. The curve starts from the second quadrant, intersects the x axis at (negative 2 comma 0) and bends at (negative 1 comma negative 3), and reaches (0 comma 0). From there, the curve moves down and turns at the point (1 comma negative 3), then goes up to intersect the x-axis at (2 comma 0), and further, it rises.
B
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has v shaped curve h of x that originates from (2 comma 0). The left side line intersects the y-axis at (0 comma 2) and enters the second quadrant. The right side line passes through (5 comma 3) and ends in the first quadrant.
C
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve k of x, starts from the third quadrant, passes through (0 comma 0), touches the x axis at (2 comma 0), and goes through (3 comma 4).
D
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1.The graph has a curve g of x starts from the second quadrant intersects the x axis at (negative 4 comma 0) then goes down and passes through (0 comma 0), (1 comma 1), (3 comma 1), and (4 comma 0) and ends in the fourth quadrant.
10

Which graph represents an even function?

A
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a parabola that opens down with a vertex at (0 comma 4). It goes through (negative 2 comma 0) and (2 comma 0).
B
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a straight line with a negative slope. It goes through (negative 2 comma 4), crosses the y axis at (0 comma 2), and crosses the x axis at (2 comma 0).
C
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has 2 curves, one in quadrant 1 and the other in quadrant 3. The curve in quadrant 1 goes through points (1 comma 5) and (5 comma 1). The curve in quadrant 3 goes through points (negative 5 comma negative 1) and (negative 1 comma negative 5).
D
Image with description On a coordinate plane, the x and y axes range from negative 5 to 5 in increments of 1. The graph has a curve in the shape of W. It has four x intercepts at (negative 2 comma 0), (negative 1 comma 0), (2 comma 0), (3 comma 0), and a y intercept at (0 comma 2 point 5). The curve has asymptotes at x equals negative 3 and x equals 4. The curve is labeled as g of x.

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Symmetry — Quiz Answers — Algebra II