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Part I - Proofs Recall the following definitions from algebra regarding even and odd functions: • A function f(x) is even if f(-x) = f(x), for each x in the domain of f. • A function f(x) is odd if f(-x) = -f(x), for each x in the domain of f. Also, keep in mind for future reference that the graph of an even function is symmetric about the y-axis and the graph of an odd function is symmetric about the origin. The following show that the given algebraic function f is an even functions. In Project 2 you will need to show whether the basic trigonometric functions are even or odd. Statement: Show that f(x) = 3x² − 2x² + 5 is an even function. Proof: If x is any real number, then f(-x) = 3(-x)4-2(-x)² +5 = 3x² - 2x² + 5 = f(x) and thus fis even. Now you should prove the following in a similar manner. (1) (2) Statement: If g(x) = 2x5 - 7x³ + 4x, show that g is an odd function. Statement: Determine whether h(x) = √25 - x² is either even or odd.

Part I - Proofs Recall the following definitions from algebra regarding even and odd functions: • A function f(x) is even if f(-x) = f(x), for each x in the domain of f. • A function f(x) is odd if f(-x) = -f(x), for each x in the domain of f. Also, keep in mind for future reference that the graph of an even function is symmetric about the y-axis and the graph of an odd function is symmetric about the origin. The following show that the given algebraic function f is an even functions. In Project 2 you will need to show whether the basic trigonometric functions are even or odd. Statement: Show that f(x) = 3x² − 2x² + 5 is an even function. Proof: If x is any real number, then f(-x) = 3(-x)4-2(-x)² +5 = 3x² - 2x² + 5 = f(x) and thus fis even. Now you should prove the following in a similar manner. (1) (2) Statement: If g(x) = 2x5 - 7x³ + 4x, show that g is an odd function. Statement: Determine whether h(x) = √25 - x² is either even or odd.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 78E
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Part I - Proofs Recall the following definitions from algebra regarding even and odd functions: • A function f(x) is even if f(-x) = f(x), for each x in the domain of f. • A function f(x) is odd if f(-x) = -f(x), for each x in the domain of f. Also, keep in mind for future reference that the graph of an even function is symmetric about the y-axis and the graph of an odd function is symmetric about the origin. The following show that the given algebraic function f is an even functions. In Project 2 you will need to show whether the basic trigonometric functions are even or odd. Statement: Show that f(x) = 3x² − 2x² + 5 is an even function. Proof: If x is any real number, then f(-x) = 3(-x)4-2(-x)² +5 = 3x² - 2x² + 5 = f(x) and thus fis even. Now you should prove the following in a similar manner. (1) (2) Statement: If g(x) = 2x5 - 7x³ + 4x, show that g is an odd function. Statement: Determine whether h(x) = √25 - x² is either even or odd.
Transcribed Image Text:Part I - Proofs Recall the following definitions from algebra regarding even and odd functions: • A function f(x) is even if f(-x) = f(x), for each x in the domain of f. • A function f(x) is odd if f(-x) = -f(x), for each x in the domain of f. Also, keep in mind for future reference that the graph of an even function is symmetric about the y-axis and the graph of an odd function is symmetric about the origin. The following show that the given algebraic function f is an even functions. In Project 2 you will need to show whether the basic trigonometric functions are even or odd. Statement: Show that f(x) = 3x² − 2x² + 5 is an even function. Proof: If x is any real number, then f(-x) = 3(-x)4-2(-x)² +5 = 3x² - 2x² + 5 = f(x) and thus fis even. Now you should prove the following in a similar manner. (1) (2) Statement: If g(x) = 2x5 - 7x³ + 4x, show that g is an odd function. Statement: Determine whether h(x) = √25 - x² is either even or odd.
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