# Explain the meaning of each type of symmetry.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 27RCC

a.

To determine

## Explain the meaning of each type of symmetry.

Expert Solution

The graph is reflect over the xaxis it will appear unchanged.

### Explanation of Solution

Given information:

Explain the meaning of each type of symmetry. How do you test for it? Symmetry with respect to the xaxis .

Calculation:

Graph of any function can have certain symmetrical properties that have both graphical and algebraic meaning.

A graph can be symmetrical with respect to xaxis , meaning that if the graph is reflect over the xaxis it will appear unchanged.

On comparing reflecting over xaxis graph with original graph if both plots are same then the function is symmetrical over xaxis otherwise it is not.

Hence, the graph is reflect over the xaxis it will appear unchanged.

b.

To determine

### Explain the meaning of each type of symmetry.

Expert Solution

The graph is reflect over the xaxis it will appear unchanged.

### Explanation of Solution

Given information:

Explain the meaning of each type of symmetry. How do you test for it? Symmetry with respect to the yaxis .

Calculation:

Graph of any function can have certain symmetrical properties that have both graphical and algebraic meaning.

A graph can be symmetrical with respect to yaxis , meaning that if the graph is reflect over the yaxis it will appear identical. this property is known as being an “even function”.

We can define this property algebraically by the condition:

f(x)=f(x) for all x in the domain of the function.

On comparing reflecting over yaxis graph with original graph if both plots are same then the function is symmetrical over yaxis otherwise it is not.

Hence, the graph is reflect over the yaxis it will appear unchanged.

c.

To determine

### Explain the meaning of each type of symmetry.

Expert Solution

The graph is rotate 180° about the origin it will appear unchanged

### Explanation of Solution

Given information:

Explain the meaning of each type of symmetry. How do you test for it? Symmetry with respect to the origin.

Calculation:

Graph of any function can have certain symmetrical properties that have both graphical and algebraic meaning.

A graph can be symmetrical with respect to origin, if we consider such a graph as representing a function, then the function is said to be an “odd function.”

Algebraically

f(x)=f(x) for all x in the domain of the function.

To test for symmetrical with respect to origin graphically, rotate the function 180° and compared it with the original plot if both plots are same than the graph has symmetry about the origin.

Hence, the graph is rotate 180° about the origin it will appear unchanged.

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