Question

What is the graph of the function g(x)=x^2-x/x^2-1?

Answer 1

Step-by-step explanation:

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Up

Vertex:

(

0

,

−

2

)

Focus:

(

0

,

−

7

4

)

Axis of Symmetry:

x

=

0

Directrix:

y

=

−

9

4

x

y

−

2

2

−

1

−

1

0

−

2

1

−

1

2

2

Tap to view steps...

image of graph

Answer 2

The graph represents a horizontal asymptote.

Step-by-step explanation:

According to the given information, it is given that the function g(x) has been defined as g(x) = $\frac{x^{2}-x }{x^{2} -1}$.

Now, this expression in the definition of g(x) can be simplified appropriately.

The simplification is,

g(x) = $\frac{x^{2}-x }{x^{2} -1}$.

Or, g(x) = $\frac{x(x-1)}{(x+1)(x-1)}$

This happens because of the well - known algebraic identity that is if a and b are two integers, then we have, a²-b² = (a+b)*(a-b).

Now, g(x) thus becomes more simplified by cancelling the term (x-1) from both the numerator and the denominator.

Then, we have,

g(x) = $\frac{x}{x+1}$

Now, when x = 0, the value of g(x) is, g(0) is equal to 0.

Now, when x = 1, the value of g(x) is, g(1) is equal to $\frac{1}{2}$.

Proceeding further, we find out the points to plot the graph of g(x) = $\frac{x}{x+1}$.

Thus, after drawing the graph, we found out that the graph represents a horizontal asymptote.

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