Graphing Exponential Functions

exponential functions

When graphing exponential functions, there are three things that you should remember.

1. All exponential functions are CURVED.
2. As the base increases, the graph shifts to the left of the y-axis.
3. If you have a negative exponent, you must rewrite your base as a fraction.

ex. (1/2)^-2  would be rewritten as 1/1/2^2 = 4

**Remember, exponential functions are never straight lines. If your graph resembles a straight line, it is a linear function.

 

Multiplying Binomials- Using the FOIL METHOD

Last week, we learned how to multiply monomials, now we will learn how to multiply binomials. Bionomials are expressions with two terms. When you multiply bionomials, you can use an algorithm called the FOIL method.

Foil is an acronym for…

First

Outside

Inside

Last

The first term is the first numbers that you see in each set of parentheses. The outside term is the first number in the first parentheses and the last number in the second parentheses. The inner term is the last term of the first parentheses and the first term of the last parentheses. Finally, the last term is the second numbers in each parentheses.

ex.  (x + 5 ) (x- 6 )  Remember, you should always multiply your terms

First term:  x*x = x^2

Outer term: x * -6 = -6x

Inner term: 5 * x =5x

Last term: 5 * -6= -30

Combine your inner and outer terms- -6x + 5x = -x

Rewrite your final answer: x^2 -x – 30

Blog Ideas and Letters to your tutors

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Remember, DO THE MATH : )!

Factoring:Greatest Common Factor

There is a factoring that is easier than FOIL and that is called the GCF or the Greatest Common Factor. The greatest common factor is a number that divisible by a set of numbers. For instance, the gcf of 12 and 18 is 6 because 12/6 = 2 and 18/6 = 3.

Well, what if there isn’t any coefficients? What if there is only variables and exponents? The same rules apply. For example, if I were to find the greatest common factor between x^3 and x^2, I must factor each term and eliminate my Xs.

ex.  x^3=  x* x* x    and x^2 = x * x

eliminate  x*x*x and x*x

The greatest common factor between these two terms is x^2.

Remember the factor BOX that Ms. Umeh showed in class?

First box: first term

Second box: second term

Third box: third term

If your middle term is a negative, your operations when you factor must also be negative. If your last term is negative, then your operations must be addition and subtraction.

 

If you need additional help, come to lunch tutoring.

Multiplying positive/negative binomials with coefficients

Image by wonderferret via Flickr

What is FOIL?’

First   Outside   Inside   Last

There are two methods to use when multiply positive and negative binomials

( x + 7 )  (x – 7 )

How to Graph a Polynomial

The Smiling Man (or Monkey Face) or the Box 

1. Multiply the coefficients for all terms.

2. Combine the outer and inner terms.