Wednesday, September 25, 2013

An easy way to graph logarithmic functions, exponential functions and square root functions is to know the basic graph of the parent functions, then shift accordingly.

f(x) = sqrt(x), f(x) - sqrt(x) flips across the x axis,  f(x) = sqrt(-x) flips across the y-axis

f(x) = sqrt(x - h) shifts h units to the right,  f(x) = sqrt(x +h) shifts h units to the left,  f(x) = sqrt(x + h) + k shifts h units left and k units up,  f(x) = sqrt(x) - k, shifts k units down.

The shifts and flips are very similar with f(x) = log(x), f(x) = e^x, etc.

Friday, September 20, 2013

This is actually quite easy, just a simple mathematical pattern.

4 would equal 12
2 would equal 2
1 would equal 0

Do you know what 3 equals?

Wednesday, September 18, 2013

There is an easy way to determine the domain of a function.  If the denominator is 1 and there are no radicals in the numerator, the domain is all real numbers.

If there is a variable in the denominator and no radical in the denominator, the domain is all real numbers except the value of x that will give a zero in the denominator.

If there is a radical with an even root, square root, fourth root, etc.  You have to solve for x such that the value under the radical is greater than or equal to zero. The domain is all real numbers except for that value.

If there is a radical with an odd root, then the domain is all real numbers.

Saturday, September 14, 2013

This one is good, hopefully everyone understands the punchline.

Thursday, September 12, 2013

Remember there are several ways to go about graphing a line.

From the equation you can plot the y-intercept and use the slope to find another point on the line.

For example, for the equation y = 2x + 4, the y-intercept if 4 and the slope is 2.  Plot a point at (0,4) and use the slope to move up 2 and to the right 1 and plot another point at (1,6).  Now draw a line through the points.

You can also find both intercepts by putting 0 in for x and then 0 in for y. Using the equation above, you get 0 = 2x + 4, therefore x = -2.  The x-intercept is -2, so plot a point at (-2,0).  Putting a 0 in for x we get y = 2(0) + 4, so the y-intercept is (0,4). Plot that point and draw a line through the points.

You can also pick any 2 values for x and find the corresponding y values. For y = 2x +4, suppose we pick 1 for x, therefore y = 6.  Now pick x =2 and you get y = 8.  Plot points at (1,6) and (2,8) and draw a line through the points.

Thursday, September 5, 2013

Here's some good math jokes.

Q: Why do they never serve beer at a math party? A: Because you can't drink and derive... Q: Why didn't the quarter roll down the hill with the nickel? A: Because it had more cents. Q: Did you hear about the constipated mathematician? A: He worked it out with a pencil. Q: How many molecules in a bowl of guacamole? A: Avacado's Number Q: What happened to the plant in math class? A: It grew square roots. Q: Why did the chicken cross the mobius strip? A: To get to the same side. Q: How do you make seven an even number? A: Take the s out! Q: Why should the number 288 never be mentioned? A: It's two gross. Q: Why couldn't the moebius strip enroll at the school? A: They required an orientation. Q: What does a mathematician do about constipation? A: He works it out with a pencil. Q: Why is a math book always unhappy? A: Because it always has lots of problems. Q: Why don't you do arithmetic in the jungle? A: Because if you add 4+4 you get ate! Q: Why did I divide sin by tan? A: Just cos. Q: Where do math teachers go on vacation? A: To Times Square. Q: Why is 6 afraid of 7? A: Because 7 8 9 Q: What does the zero say to the the eight? A: Nice belt! Q: Why did the mutually exclusive events break up? A: They had nothing in common. Q: How is an artificial christmas tree like the fourth root of -68? A: Neither has real roots.


Tuesday, September 3, 2013

Just a question to ponder. In most high school math sequences, algebra is followed by geometry, second year algebra, pre-calculus, (which involves trigonometry), then calculus, or statistics.

Why is not algebra II immediately following algebra I?  Geometry and trigonometry work hand in hand, so why not bunch those two back to back following the algebra courses?