# Thread: XY Graph for Inverse Function?

1. ## XY Graph for Inverse Function?

I need to graph $\displaystyle y=x^2+4$.
I understand subbing in values for X to get Y. The graph is a positive (opens upwards) parabola.
The inverse would be. $\displaystyle y=\pm \sqrt {x-4}$

As for graphing, I usually use x values of -3,-2,-1,0,1,2,3.
Do I substitute those values into the inverse equation the same I would the regular function?
If I sub the value of 0 in for X, then X-4 = -4. Then nothing is the square of -4.
How do I calculate to find Y properly, when working with an inverse equation?

2. Originally Posted by NotSoBasic
I need to graph $\displaystyle y=x^2+4$.
I understand subbing in values for X to get Y. The graph is a positive (opens upwards) parabola.
The inverse would be. $\displaystyle y=\pm \sqrt {x-4}$

As for graphing, I usually use x values of -3,-2,-1,0,1,2,3.
Do I substitute those values into the inverse equation the same I would the regular function?
If I sub the value of 0 in for X, then X-4 = -4. Then nothing is the square of -4.
How do I calculate to find Y properly, when working with an inverse equation?
The domain of inverse function is

$\displaystyle x \ge 4$

so, you cannot put the values which are less than 4. The inverse is not defined for those values.

3. Originally Posted by Shyam
The domain of inverse function is

$\displaystyle x \ge 4$

so, you cannot put the values which are less than 4. The inverse is not defined for those values.
I've used an applet to graph and see how the domain is
$\displaystyle x \ge 4$

Is there someway to find out what values of x to start with when I don't have access to an applet, or do I just use trial and error until I find a number that can be squared?
So now I can substitute values into x, and I would assume that I should only use the y values which end up as a whole number, ie.
if x = 8, then $\displaystyle y=\pm\sqrt {8-4}$ which then equals $\displaystyle y=\pm2$

Is making an xy graph possible for inverse, how do I properly show the values on paper before I attempt to graph the points?

4. Or to get my points for the inverse I just switch the x<=>y from my original xy table? That would seem to make sense, since it is an inverse. =P

From there $\displaystyle x \ge 4$ because y=0 on the inverse?

5. Originally Posted by NotSoBasic
I need to graph $\displaystyle y=x^2+4$.
I understand subbing in values for X to get Y. The graph is a positive (opens upwards) parabola.
The inverse would be. $\displaystyle y=\pm \sqrt {x-4}$

As for graphing, I usually use x values of -3,-2,-1,0,1,2,3.
Do I substitute those values into the inverse equation the same I would the regular function?
If I sub the value of 0 in for X, then X-4 = -4. Then nothing is the square of -4.
How do I calculate to find Y properly, when working with an inverse equation?
Since $\displaystyle x^2$ is never negative, $\displaystyle y= x^2+ 4$ is never negative. The function $\displaystyle y= x^2+ 4$ has domain "all real numbers" and range "all real numbers larger than or equal to 4".

The inverse function reverses domain and range. The inverse function would have domain "all real numbers larger than or equal to 4" and range "all real numbers". The fact that the domain is "all real numbers large than or equal to 4" is why you cannot put, say, x= 3 or x= 2, in for x.

Of course, this function, $\displaystyle x^2+ 4$ is not "one-to-one" and so does not have a true inverse. You have to break it into two functions, $\displaystyle y= \sqrt{x- 4}$ and $\displaystyle y= -\sqrt{x- 4}$ in order to get the entire range of "all real numbers".

6. Great, thanks guys!
I'm doing this stuff from home on my own, and having your assistance to explain things not in my given documents is very much appreciated!

7. Her is another way to plot the graph of an inverse function:

STEP 1:Plot the graph of the given function.

STEP 2:Plot the reflection of the graph drawn with respect to the line $\displaystyle y=x$ acting as mirror.

And you have the graph of the inverse function.