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An equation is symmetric with respect to the $x$ -axis if replacing $y$ by $-y$ leaves the equation unchanged. (a) Why can't such an equation represent a function? (b) In Exercise $24-29,$ which of the equations has this symmetry?

(a) violates vertical line test(b) Exercises 25 and 27

Algebra

Chapter 1

Functions and their Applications

Section 7

More on Functions

Functions

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Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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01:04

An equation is symmetric w…

00:39

Explain why the graph of a…

00:41

For a curve to be symmetri…

00:36

An odd function is symmetr…

01:11

00:52

Multiple Choice To test wh…

to answer this question, we need first to review the definition off function. This definition comes from sector 1.2 at page 60. Off this test book function is a set off ordered pairs obtained by some rules so that each first element in the ordered pair there corresponds a unique second element in the other pair here. The first element is acts in the second element is why so if an equation is symmetric with respect to the X axis for a certain ex, both the corresponding why and matters why satisfies the equation, which says there are at least two wise in the other pair? And this well, it the definition of the function for per B 25 27 uh, symmetric with respect to the X axis, since if they replace, why by manners why, it will still satisfy the equation and you can verify it by this to expressions

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