Nov. 1 Class

Today we did more examples of graphing exponential equations with transformations.  In particular we looked at vertical stretches, horizontal translations, and vertical translations.

Try to match each equation with the proper graphs in each example:

In all examples, place close attention to where the asymptotes are.  You will be expected to sketch and label the asymptotes as well.

Homework: Complete handouts.

Oct. 31 Class

Today we talked about how to graph the exponential function.

Handouts:
Graphing Exponential Functions (page 1)
Graphing Exponential Functions (page 2-3)

An exponential function is a function of the form: .

Where b is any base that is greater than zero and not equal to 1 (forgot to mention that in class!  Remind me to tell everyone tomorrow.)

The graph of  looks like the following:

Where I've highlighted some important points that you might use to graph it.

Some important features of this graph include:

• Always increasing.
• Always above zero.
• As x becomes larger, y gets very large.
• As x becomes more negative, y gets closer to zero.
• Never touches the x-axis (a horizontal asymptote).

Next we graphed , and got,

Which turns out to be a horizontal reflection of the above graph.  Points to note:

• The reciprocal of the base is the same thing as a horizontal reflection.
• The y-intercept is always 1 for any base.

Lastly, if you had a table of values and tried to calculate the first and second differences, you will not be able to tell if it's an exponential function.  Instead you must calculate the ratios of each y-value to the y-value before it.  If the ratios are constant then you have an exponential function.

Homework:

Complete the page of the handout for .

P. 243 # 1 - 2.

Oct. 30 Class

I handed out the revised copy of the current unit's daily plan.

Handout: New Daily Plan for Unit 4

As we discussed the next test will be split up over two days.

Today we discussed how to simplify algebraic expressions with exponents.

Here are the notes and examples:

We also had a discussion about negative signs and radicals with negative radicands.

Homework: P. 235 # 4 – 12

Oct. 29 Class

Today we discussed what it means to have a rational exponent.  Through some discussions I showed that 8 with exponent 1/2 is the same thing as the square root of 8.

Here are my notes:

Homework: P. 226 #1-7(eoo), 11-14 (eoo)

Oct. 26 Class

New Unit: Exponential Functions

Today we began our new unit on exponential functions.  As a review we went over the important laws of exponents.

Handout: Exponent Review

Here are the notes:

Then I went over how to solve equations where the variable is in the exponent.

Here are the notes:

 

Homework: 

Complete the handout (every other question)

P. 221  #(1,2,4–9,11,13,14,16) – b,d,f,h only

Oct. 25 Class

Congratulations on completing your test today!

The new unit on exponential functions will begin tomorrow.

Oct. 24 Class

Today we discussed some review topics for the test:

2 double sided long pages.

You should be able to:

 - Find zeroes of quadratic equations

 - Find vertex of quadratic equations

 - Find the equation of the axis of symmetry

 - Find maximum or minimum

Techniques:

 - Complete the square

 - Formula (x = -b/2a)

 - Quadratic Formula

 - Factoring to find zeros

 - Averaging the roots

 - Partial factoring

Know how to simplify radicals.

Know how to determine the nature of the roots of a quadratic equation.

Know how to solve linear quadratic systems.

Know how to solve word problems.

 - Cost / Revenue / Profit type

 - Area type

 - Speed type

 - Projectile type

 - "Find the numbers" type

Here are some solutions to word problems that I worked out in class:

Good luck in your studies!