Par function
We will study the way in which the function is constituted f (x) = x² - 1, represented on the Cartesian graph. Note that in the function, we have:
f(1) = 0; f(–1) = 0 and f(2) = 3 and f(–2) = 3.
f(–1) = (–1)² – 1 = 1 – 1 = 0
f (1) = 1² - 1 = 1 - 1 = 0
f(–2) = (–2)² –1 = 4 – 1 = 3
f(2) = 2² - 1 = 4 - 1 = 3
Note from the graph that there is symmetry with respect to the y axis. The images of domains x = – 1 and x = 1 correspond with y = 0 and domains x = –2 and x = 2 form ordered pairs with the same image y = 3. For symmetric domain values, the image assumes the same value. We give this type of occurrence the even function classification.
A function f is considered even when f(–x) = f(x), whatever the value of x Є D(f).
unique function
We will analyze the function f (x) = 2x, according to the graph. In this function, we have that: f(–2) = – 4; f(2) = 4.
f(–2) = 2 * (–2) = – 4
f(2) = 2 * 2 = 4
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Look at the graph and visualize that there is symmetry in relation to the point of origins. On the abscissa (x) axis, we have the symmetric points (2;0) and (–2;0), and on the ordinate axis (y), we have the symmetric points (0.4) and (0;–4). In this situation, the function is classified as odd.
A function f is considered odd when f(–x) = – f (x), whatever the value of x Є D(f).
by Mark Noah
Graduated in Mathematics
Brazil School Team
Occupation - Math - Brazil school
Would you like to reference this text in a school or academic work? Look:
SILVA, Marcos Noé Pedro da. "Even Function and Odd Function"; Brazil School. Available in: https://brasilescola.uol.com.br/matematica/funcao-par-funcao-impar.htm. Accessed on June 28, 2021.
