2. Here are some more examples of Reciprocal functions. To view the next slide press the spacebar. To quit the show press escape.

3. Example 1 of a Reciprocal Function Original Y-values of zero result in vertical asymptotes for the reciprocal Original negative y-values result in reciprocals that are negative (the reciprocal will not cross the x-axis) Where the original was decreasing, the reciprocal is increasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values – don’t forget we talked about the absolute value) Where the original was decreasing, the reciprocal is increasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values) Original Y-values of 1 and –1 don’t change Original positive y-values result in reciprocals that are positive (the reciprocal will not cross the x-axis) First draw y= - x +2, which is a straight line with slope -1 and y-int 2. We did it! The graph hugs the asymptotes

4. Here is a better picture of the function

5. Example 2 of a Reciprocal Function Original Y-values of zero result in vertical asymptotes for the reciprocal Where the original was increasing, the reciprocal is decreasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values Where the original was decreasing, the reciprocal is increasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values) Original Y-values of 1 and –1 don’t change Original positive y-values result in reciprocals that are positive (the reciprocal will not cross the x-axis) First draw y=-x 2, which is a parabola with vertex at (0,0). We did it! It kind of looks like a skinny volcano. The graph hugs the asymptotes

6. Here is a more accurate graph.

7. Example 3 of a Reciprocal Function Original Y-values of zero result in vertical asymptotes for the reciprocal. But for this one the original function does not have any y-values of zero, so there are no vertical asymptotes. Where the original was increasing, the reciprocal is decreasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values Where the original was decreasing, the reciprocal is increasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values) Original Y-values of 1 and –1 don’t change But for this one there are no y-values of 1 or –1. So we take the reciprocal of the vertex which would be ½. Original positive y-values result in reciprocals that are positive (the reciprocal will not cross the x-axis) First draw y=-x 2, which is a parabola with vertex at (0,0). We did it! It kind of looks like a speed bump. The graph hugs the asymptotes

8. Here is a more accurate graph

9. Another Example of a Reciprocal Function Original Y-values of zero result in vertical asymptotes for the reciprocal Where the original was increasing, the reciprocal is decreasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values Where the original was decreasing, the reciprocal is increasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values) Original Y-values of 1 and –1 don’t change Original positive y-values result in reciprocals that are positive (the reciprocal will not cross the x-axis) First draw y=-x 2, which is a parabola with vertex at (0,0). Then shift the parabola two units to the right. We did it! It kind of looks like a skinny volcano. But shifted two units right. The graph hugs the asymptotes

10. Here is a more accurate graph.

11. Another Example of a Reciprocal Function Original Y-values of zero result in vertical asymptotes for the reciprocal Where the original was increasing, the reciprocal is decreasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values Where the original was decreasing, the reciprocal is increasing (original big y-values result in reciprocal small y-values; original small y-values result in reciprocal big y-values) Original Y-values of 1 and –1 don’t change Original positive y-values result in reciprocals that are positive (the reciprocal will not cross the x-axis) First draw y=-x 2, which is a parabola with vertex at (0,0). Then shift the parabola four units down. We did it! It kind of looks like a pig – a pig? See the next slide to see what I Mean. The graph hugs the asymptotes Original negative y-values result in reciprocals that are negative (the reciprocal will not cross the x-axis)

12. It looks like a pig! Or a dog or whatever you can imagine – just come up with something to help you remember.