Symmetry Algebra 2 B Flashcards

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)

Which graphs have rotational symmetry? (Select all that apply)

If f is an even function, what is the value of a?

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) = ____

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 odd function shown in the graph.

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 increasing for which value?

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^2 represent 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 f behaves in specific intervals:
- Interval 0 < x < 2: Function is increasing, with f(2) = 3.
- Interval 2 < x < 5: Function is decreasing.

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 and g(x) is odd, the classification yields:
- From g: odd.
- From f: even.

Function Traits

Constant nature for the function in the interval -9 < x < -7.
Increasing function behavior starts at x = -7.

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.