The question goes as:

**Sketch the graph of a function f that satisfies all of the following conditions:**

*limit of f(x) as x approaches 3 equals negative infinity*

*limit of f(x) as x approaches infinity equals 2*

*f(0)=0*

*f is even*

*--------------------------*

Also when they say *"f is even" *, is it the same as saying **f(x) = x²** ?

chilledz3non
Sep 18, 2014

#1**+10 **

Ane even function is one where f(x)=f(-x)

When you graph is it will be symmetrical about the y axis.

$$f(x)=x^2$$ is an example of an even function because f(x)=f(-x) eg f(3)=9 f(-3)=9

There is more than one graph that will fit this description.

but here is one of them.

Perhaps one of the other mathematicians can tell me what the equation of a graph like this might be?

I really have no idea.

Melody
Sep 19, 2014

#1**+10 **

Best Answer

Ane even function is one where f(x)=f(-x)

When you graph is it will be symmetrical about the y axis.

$$f(x)=x^2$$ is an example of an even function because f(x)=f(-x) eg f(3)=9 f(-3)=9

There is more than one graph that will fit this description.

but here is one of them.

Perhaps one of the other mathematicians can tell me what the equation of a graph like this might be?

I really have no idea.

Melody
Sep 19, 2014

#2**0 **

Thanks so much Melody. At first I just drew out a bunch of different graphs and got stuck at when I was going to graph the "even function". You're a life-saver haha xD

chilledz3non
Sep 19, 2014