Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 2 - Functions and GraphsProblema 26
Capitolo 3, Problema 26

Determine whether each graph is the graph of an even function, an odd function, or a function that is neither even nor odd.
Graph showing a curve in the first and fourth quadrants, illustrating a function's behavior.

Guida verificata passo dopo passo
1
Observe the graph and note that the curve is present in the first and fourth quadrants, and it does not touch or cross the origin.
To determine if the function is even, check if the graph is symmetric about the y-axis. This means that for every point (x, y) on the graph, the point (-x, y) must also be on the graph. In this case, the graph is not symmetric about the y-axis.
To determine if the function is odd, check if the graph is symmetric about the origin. This means that for every point (x, y) on the graph, the point (-x, -y) must also be on the graph. In this case, the graph is not symmetric about the origin.
Since the graph is neither symmetric about the y-axis nor the origin, the function is neither even nor odd.
Conclude that the function represented by the graph is neither even nor odd based on the symmetry analysis.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Even Functions

An even function is defined by the property that f(x) = f(-x) for all x in its domain. This means that the graph of an even function is symmetric with respect to the y-axis. A common example of an even function is f(x) = x², where the values of the function are the same for both positive and negative inputs.
Video consigliato:
6:13
Exponential Functions

Odd Functions

An odd function satisfies the condition f(-x) = -f(x) for all x in its domain. This indicates that the graph of an odd function is symmetric with respect to the origin. A classic example of an odd function is f(x) = x³, where the function values for positive and negative inputs are equal in magnitude but opposite in sign.
Video consigliato:
06:08
End Behavior of Polynomial Functions

Neither Even Nor Odd Functions

A function is classified as neither even nor odd if it does not meet the criteria for either category. This means that the function does not exhibit symmetry about the y-axis or the origin. An example of such a function could be f(x) = x + 1, where the graph does not reflect any of the properties of even or odd functions.
Video consigliato:
06:08
End Behavior of Polynomial Functions
Pratica correlata
Domanda del libro di testo

Find the domain of each function. h(x) = √(x −2)+ √(x +3)

889
views
Domanda del libro di testo

Find the midpoint of each line segment with the given endpoints. (-7/2, 3/2) and (-5/2, -11/2)

924
views
Domanda del libro di testo

Find the midpoint of each line segment with the given endpoints. (8, 3√5) and (−6, 7√5)

808
views
Domanda del libro di testo

Use the graph of y = f(x) to graph each function g. g(x) = -f(x)+1

595
views
Domanda del libro di testo

The functions in Exercises 11-28 are all one-to-one. For each function, a. Find an equation for f-1(x), the inverse function. b. Verify that your equation is correct by showing that f(ƒ-1 (x)) = = x and ƒ-1 (f(x)) = x. f(x) = (2x +1)/(x-3)

599
views
Domanda del libro di testo

Determine whether each equation defines y as a function of x. |x|- y = 5

1000
views