Questions and Answers
Which of these functions are odd? (Select all that apply)
Which graphs have a line of symmetry? (Select all that apply)
Which functions are symmetric about the y-axis? (Select all that apply)
Which functions are even? (Select all that apply)
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Which graphs have rotational symmetry? (Select all that apply)
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If f is an even function, what is the value of a?
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If g is an odd function, what is the value of b?
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The function f is over the interval 0 < x < 2. Complete: f(2) = ____
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Describe the symmetry of these functions. (Select all that apply)
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Complete the table of values for the even function shown in the graph.
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Complete the table of values for the odd function shown in the graph.
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Determine whether each function is even, odd, or neither. (Select all that apply)
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Given that f(x) is even and g(x) is odd, determine whether each function is even, odd, or neither. (Select all that apply)
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The function is for which range: -9 < x < -7?
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The function is increasing for which value?
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Study Notes
Functions and Symmetry
-
Odd Functions:
f(x) = x^5 - 3x^3 + 2x,f(x) = 1/x - Line Symmetry: Graphs from the first and third quadrants have line symmetry.
- Y-axis Symmetry: First and third functions are symmetric about the y-axis.
-
Even Functions:
f(x) = |x|,f(x) = x^4 - x^2represent even functions.
Types of Graph Symmetry
- Rotational Symmetry: Graphs from the first and third quadrants exhibit rotational symmetry.
-
Even Function Properties: For an even function,
a = 4. -
Odd Function Properties: For an odd function,
b = 3.
Graph Behavior
- Function
fbehaves in specific intervals:-
Interval 0 < x < 2: Function is increasing, with
f(2) = 3. - Interval 2 < x < 5: Function is decreasing.
-
Interval 0 < x < 2: Function is increasing, with
Function Symmetry Description
- Functions can have properties:
- Line Symmetry only.
- Rotational Symmetry only.
Graph Value Completion
-
Even Function Values: Table values from the graph indicate symmetry:
f(1) = 1,f(3) = 3. -
Odd Function Values: Values from the graph show:
g(-2) = -2,g(-1) = -3.
Function Classification
- Each function can be classified as:
- Even
- Odd
- Neither
Combined Function Attributes
- Given
f(x)is even andg(x)is odd, the classification yields:- From
g: odd. - From
f: even.
- From
Function Traits
- Constant nature for the function in the interval
-9 < x < -7. - Increasing function behavior starts at
x = -7.
Studying That Suits You
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Description
Test your knowledge of symmetry in functions and graphs with these flashcards. Determine which functions are odd, even, or symmetric about the y-axis and identify graphs with lines of symmetry. Perfect for Algebra 2 students looking to reinforce their understanding of symmetry concepts.
