11 SL Laws of Logarithms

Use the laws of logarithms to answer the following questions for the start of our next class on Thursday.

Exercise 4C.1 questions 1adghko, 2adg, 3ad, 4de, 5ad, 6abde, 7c Exercise 4C.2 questions 1aef, 2ace, 4abd
Exercise 4D.1 questions 1, 2, 4, 6abef
Exercise 4D.2 questions 1abhk, 2ae, 4ab, 5b

11 SL Logarithms

Complete the following questions for our next class.

Exercise 4A questions 1, 2, 6
Exercise 4B questions 1ade, 2adgh, 3abjmqrs, 4, 5, 6acdfgmn

11 SL Modelling with Exponential Functions

Complete the following questions for our class tomorrow. We’ll have a short (1 question) quiz on this material tomorrow. Remember, if you get stuck, just post a comment below!

Exercise Set 3G.1 questions 1–3
Exercise Set 3G.2 questions 1, 4, 5

11 SL Exponential Functions

In class we looked at functions of the form \(f(x)=a\cdot b^x+d\), and we had a brief discussion of the effect of the values of \(a, b,\) and \(c\) on the graph of the function. Below, you’ll extend this treatment to understand the effect of the values of  \(a, b, c,\) and \(d\) on the graph of functions of the form \(f(x)=a\cdot b^{x-c}+d\).

Read through Investigation 1 on page 95 of the textbook, and use graphing software (I suggest either GeoGebra or Desmos) to explore the effects of various values on the graph of each function. As discussed in class, using sliders can make it easier to see the effect of each, and you can see an example of this below. (But it’s more fun to try to make your own version of this!)

Once you’ve completed your investigation, complete questions 4 and 5 from Exercise 3F. (Record your answers in your notebook, and then bring your notebook to class!)

11 SL Exponents

Remember to complete the following questions for our lesson tomorrow.

Exercise Set 3A questions 3 and 4
Exercise Set 3B questions 3–5
Exercise Set 3C questions 3, 5

11 SL Rational Functions

Your homework for tonight involves work with sign diagrams and rational functions.

Read through Example 9 on sign diagrams on page 68, and see if you can answer the assigned parts of question 2 and 3 (see below) without graphing the given function.

Also read through the textbook section on rational functions (2F), paying particular attention to the discussion of asymptotes. Note that the textbook’s definition of a rational function is actually more limited that the (correct) definition we’ve used, which is how they avoid talking about polynomials in this section.

Complete all of the section 2E questions listed below, and as many of the questions below from 2F as you are able.

Exercise 2E questions 1fhk, 2adg, 3agh
Exercise 2F questions 1bc, 2ab