Graphing Reciprocal Functions, Absolute Values and Trig Reciprocals Review

(March 16,2011)

Todays class was extremely productive. We covered almost three exercises in under two hours. (YAY!) In the morning, we finished off the notes from exercise 10(graphing reciprocal functions), and Graphing Absolute Values(exercise 11) and in the afternoon, got right into Graphing Trig Reciprocals. Summary of todays notes will be posted down below so keep reading. =)

Exercise 10: Graphing Reciprocal Functions

Steps in graphing a reciprocal function:

• First of all, make sure you use the reciprocal of the function instead of the original one.

• Next, you have to find the asymptote. To do this you have take the denominator (-x/2-2) and set y to 0:
• ( 0=-x/2-2 and solve for "x")

• Once you have "x" you can then draw in your asymptote with a dotted line (in this case x=-4, so our asymptote=-4
• Then find the invariant points(turn points). ***Remember in reciprocal graphs, the invariant points are located at y=1 & y=-1 (Again take the denominator and set y to -1 and 1) 1=-x/2-2 and -1=-x/2-2 then solve for "x".
• Next plot these points and graph the reciprocal function

Exercise 11: Graphing Absolute Values

The easiest way to graph absolute values is to make a table of values.

- But remember that the absolute value of a function is always positive or zero. So all the points that are below the x-axis(-ve points) get reflected to above the x-axis.

Your new table of values should look like

this:

- Next just plot the points in the graph and connect the dots.

NO NEGATIVE "Y" VALUES

Graphing Trig Reciprocals:

Example:Graph a Cosecant Graph (We all know from the previous unit that Cosecant is the reciprocal of sin. (Cosecant= 1/sinx)

-Start off by graphing your typical y=sinx graph

-Indentify your asymptotes (where y=0) and draw them on the graph with dotted lines

(Asymptotes for this graph would be: -2π,-π, 0, π and 2π)

- Find the Invariant points again (where sin=1 or sin=-1) in this case they are

-3π/2, -π/2,π/2,3π/2

-Lastly, determine whether sin is +ve or -ve in your invariant points.

If sin is -ve, graph will curve downwards, if it is +ve, graph will curve up

(Use the CAST rule is you have trouble remembering)

YOUR FINAL GRAPH SHOULD LOOK LIKE THIS!

That's it!.....hope these notes help.

oh and tomorrow's blogger will be NM

(cause he missed his turn)