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Section 2-2Linearity and Symmetry
Essential Questions
• How do you identify linear and nonlinear functions by examining equations or graphs?
• How do you determine whether graphs of functions have line or point symmetry?
Vocabulary1. Linear Equation:
2. Linear Function:
3. Nonlinear Function:
4. Line Symmetry:
Vocabulary1. Linear Equation: An equation that represents a
line where the highest power of a variable is 1
2. Linear Function:
3. Nonlinear Function:
4. Line Symmetry:
Vocabulary1. Linear Equation: An equation that represents a
line where the highest power of a variable is 1
2. Linear Function: When a linear equation is written in function notation
3. Nonlinear Function:
4. Line Symmetry:
Vocabulary1. Linear Equation: An equation that represents a
line where the highest power of a variable is 1
2. Linear Function: When a linear equation is written in function notation
3. Nonlinear Function: A function that is not linear; will have a power other than 1
4. Line Symmetry:
Vocabulary1. Linear Equation: An equation that represents a
line where the highest power of a variable is 1
2. Linear Function: When a linear equation is written in function notation
3. Nonlinear Function: A function that is not linear; will have a power other than 1
4. Line Symmetry: When a graph can be folded on top of itself
Vocabulary5. Line of Symmetry:
6. Point Symmetry:
7. Point of Symmetry:
Vocabulary5. Line of Symmetry: The line that that divides a
graph into halves that fold over on top of itself
6. Point Symmetry:
7. Point of Symmetry:
Vocabulary5. Line of Symmetry: The line that that divides a
graph into halves that fold over on top of itself
6. Point Symmetry: When a graph can be rotated 180º about a point so it ends on top of itself
7. Point of Symmetry:
Vocabulary5. Line of Symmetry: The line that that divides a
graph into halves that fold over on top of itself
6. Point Symmetry: When a graph can be rotated 180º about a point so it ends on top of itself
7. Point of Symmetry: The point that is the center of a rotation
Example 1State whether each function is a linear function. Write
yes or no. Explain.
a. g(x ) = 2x − 5 b. p(x ) = x3 + 2
c. 3y − 21x = 12
Example 1State whether each function is a linear function. Write
yes or no. Explain.
a. g(x ) = 2x − 5 b. p(x ) = x3 + 2
c. 3y − 21x = 12
Yes; highest exponent on x is 1
Example 1State whether each function is a linear function. Write
yes or no. Explain.
a. g(x ) = 2x − 5 b. p(x ) = x3 + 2
c. 3y − 21x = 12
Yes; highest exponent on x is 1
No; highest exponent on x is 3
Example 1State whether each function is a linear function. Write
yes or no. Explain.
a. g(x ) = 2x − 5 b. p(x ) = x3 + 2
c. 3y − 21x = 12
Yes; highest exponent on x is 1
No; highest exponent on x is 3
Yes; highest exponent on x is 1
Example 1State whether each function is a linear function. Write
yes or no. Explain.
a. g(x ) = 2x − 5 b. p(x ) = x3 + 2
c. 3y − 21x = 12
Yes; highest exponent on x is 1
No; highest exponent on x is 3
Yes; highest exponent on x is 1y = 7x + 4
Example 2Matt Mitarnowski and Maggie Brann work part-time at a smoothie store. The number of hours they worked increased for the first 5 weeks on
the job. The graph models Matt’s weekly earnings, and the table models Maggie’s weekly
earning for these five weeks. State whether each relation is a linear function. Explain.
Example 2Matt’s
Earnings
Earn
ings
($)
0306090
120150180210
Week0 1 2 3 4 5
Maggie’s EarningsWeek 1 2 3 4 5
Earnings ($)
60 120 180 210 240
Example 2Matt’s
Earnings
Earn
ings
($)
0306090
120150180210
Week0 1 2 3 4 5
Maggie’s EarningsWeek 1 2 3 4 5
Earnings ($)
60 120 180 210 240
Matt’s earnings are linear as a line can be drawn through the points. Maggie’s
earnings are nonlinear as the values change by different amounts
Example 3State whether the graph of the function has line symmetry. If so, identify the line of symmetry.
Example 3State whether the graph of the function has line symmetry. If so, identify the line of symmetry.
This graph has line symmetry. It can reflect over the vertical line through x = 1.
Example 4State whether the graph of the function has
point symmetry. If so, identify the point or points of symmetry.
Example 4State whether the graph of the function has
point symmetry. If so, identify the point or points of symmetry.
This graph has point symmetry. It can rotate around the point (0,3).
