Question

Which graph represents the function f(x)=2x/x^2-1

Answer 1

Solution:

we have been asked to find the graph of the equation

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

We can get the graph by simply taking some values for the variable x and working out the value of the variable y. Then we just need to put those values on the graph and connect.

when$x=-3, y=f(-3)=\frac{2\times(-3)}{(-3)^2-1}=\frac{-6}{8}=-0.75$

when$x=-2, y=f(-2)=\frac{2\times(-2)}{(-2)^2-1}=\frac{-4}{3}=- 1.33$

when$x=0, y=f(0)=\frac{2\times(0)}{(0)^2-1}=0$

when$x=2, y=f(2)=\frac{2\times(2)}{(2)^2-1}=\frac{4}{3}= 1.33$

when$x=3, y=f(3)=\frac{2\times(3)}{(3)^2-1}=\frac{6}{8}=0.75$

Also function is not defined at $x=\pm1$

Now put theses value on the graph and connect the points, we will get the graph as attached.

Answer 2

See attachment for your answer: