Podcast
Questions and Answers
Which of these functions are odd? (Select all that apply)
Which of these functions are odd? (Select all that apply)
- f(x)=x^5-3x^3+2x
- f(x)=1/x (correct)
Which graphs have a line of symmetry? (Select all that apply)
Which graphs have a line of symmetry? (Select all that apply)
- Third (correct)
- First (correct)
Which functions are symmetric about the y-axis? (Select all that apply)
Which functions are symmetric about the y-axis? (Select all that apply)
- Third (correct)
- First (correct)
Which functions are even? (Select all that apply)
Which functions are even? (Select all that apply)
Which graphs have rotational symmetry? (Select all that apply)
Which graphs have rotational symmetry? (Select all that apply)
If f is an even function, what is the value of a?
If f is an even function, what is the value of a?
If g is an odd function, what is the value of b?
If g is an odd function, what is the value of b?
The function f is over the interval 0 < x < 2. Complete: f(2) = ____
The function f is over the interval 0 < x < 2. Complete: f(2) = ____
Describe the symmetry of these functions. (Select all that apply)
Describe the symmetry of these functions. (Select all that apply)
Complete the table of values for the even function shown in the graph.
Complete the table of values for the even function shown in the graph.
Complete the table of values for the odd function shown in the graph.
Complete the table of values for the odd function shown in the graph.
Determine whether each function is even, odd, or neither. (Select all that apply)
Determine whether each function is even, odd, or neither. (Select all that apply)
Given that f(x) is even and g(x) is odd, determine whether each function is even, odd, or neither. (Select all that apply)
Given that f(x) is even and g(x) is odd, determine whether each function is even, odd, or neither. (Select all that apply)
The function is for which range: -9 < x < -7?
The function is for which range: -9 < x < -7?
The function is increasing for which value?
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.
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