Free Printable Week 2 Math 104 Symmetry (Sec1.7)

1.

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for origin symmetry?

a)

(x,y) <-> (-x, -y)

b)

(x,y) <-> (-x, y)

c)

(x,y) <-> (x, -y)

d)

(x,y) <-> (y,x)

2.

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for x-axis symmetry?

a)

(x,y) <-> (-x, -y)

b)

(x,y) <-> (-x, y)

c)

(x,y) <-> (x, -y)

d)

(x,y) <-> (y,x)

3.

A function, f(x), creates a solution set of ordered pairs {(x₁,y₁), (x₂,y₂), (x₃,y₃)...} that are usually described by an equation. A test for symmetry creates the same solution and equation by substituting a particular combination of + or - x and y.
What is the test for y-axis symmetry?

a)

(x,y) <-> (-x, -y)

b)

(x,y) <-> (-x, y)

c)

(x,y) <-> (x, -y)

d)

(x,y) <-> (y,x)

4.

Use the symmetry tests to determine the type of symmetry for: $x=y^2-4$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

5.

Use the symmetry tests to determine the type of symmetry for: $x^2+y^2=9$

(Hint: what type of equation is this for)
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

6.

Use the symmetry tests to determine the type of symmetry for: $y=3x^8-7x^2+2$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

7.

What kind of symmetry does this graph exhibit?

a)

Symmetry about the x-axis only

b)

Symmetry about the y-axis only

c)

Symmetry about the origin only

d)

Symmetry about the x-axis, y-axis, and origin.

8.

What kind of symmetry does this graph exhibit?

a)

Symmetry about the x-axis only

b)

Symmetry about the y-axis only

c)

Symmetry about the origin only

d)

Symmetry about the x-axis, y-axis, and origin.

Week 2 Math 104 Symmetry (Sec1.7)

Total questions: 8

Worksheet time: 10mins

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