How do you determine whether the graph of #g(x)=(x^2-1)/x# is symmetric with respect to the origin?

Answer 1

The graph of g(x) is symmetric with respect to the origin

The graph of g(x) is symmetric with respect to the origin if

#g(-x)=-g(x)#

that's if g(x) is an odd function , then it is:

# **g(-x)** =((-x)^2-1)/(-x)=-(x^2-1)/x **=-g(x)** #

graph{(x^2-1)/x [-5, 5, -5, 5]}

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To determine whether the graph of ( g(x) = \frac{x^2 - 1}{x} ) is symmetric with respect to the origin, we can check if the function satisfies the condition of odd symmetry.

A function ( f(x) ) is said to be odd symmetric with respect to the origin if for every point ( (x, y) ) on the graph of ( f(x) ), the point ( (-x, -y) ) is also on the graph.

To check for odd symmetry, we evaluate ( g(-x) ) and compare it to ( -g(x) ):

[ g(-x) = \frac{(-x)^2 - 1}{-x} = \frac{x^2 - 1}{-x} = -\frac{x^2 - 1}{x} = -g(x) ]

Since ( g(-x) = -g(x) ), the function ( g(x) ) satisfies the condition for odd symmetry with respect to the origin.

Therefore, the graph of ( g(x) = \frac{x^2 - 1}{x} ) is symmetric with respect to the origin.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To determine whether the graph of ( g(x) = \frac{x^2 - 1}{x} ) is symmetric with respect to the origin, you need to check if replacing ( x ) with ( -x ) in the equation results in the same function or its opposite.

[ g(-x) = \frac{(-x)^2 - 1}{-x} ]

If ( g(-x) = g(x) ), then the graph is symmetric with respect to the origin. If ( g(-x) = -g(x) ), then the graph is symmetric with respect to the origin as well.

Let's perform the substitution:

[ g(-x) = \frac{(-x)^2 - 1}{-x} ] [ = \frac{x^2 - 1}{-x} ] [ = -\frac{x^2 - 1}{x} ]

Since ( g(-x) = -g(x) ), the graph of ( g(x) = \frac{x^2 - 1}{x} ) is symmetric with respect to the origin.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7