Alg 2 Feb 27 & 28

Algebra 2
Unit 5 - Exponential & Logarithmic
Functions.

By Mr. Pousada

Standards

A.APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition,
subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational
expressions.
A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising
from simple rational functions.
A.CED.2 Create linear, quadratic, and exponential equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales. (Limit to rational and radical functions. The phrase
“in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple
variables.)
A.REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions
may arise.
F.IF.4 Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the
relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function
is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and
periodicity.
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a
specified interval. Estimate the rate of change from a graph.
F.IF.9 Compare properties of two functions, each represented in a different way (algebraically , graphically, numerically in
tables, or by verbal descriptions)
.IF.7d Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing
end behavior.
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic
expressions for them.
A.REI.11 Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the
x-value where the y-values of f(x) and g(x) are the same.

Essential Questions

●How can we extend arithmetic properties and processes to algebraic expressions and how can we
use these properties and processes to solve problems?

●How do the polynomial pieces of a rational function affect the characteristics of the function itself?

●How are horizontal asymptotes, slant asymptotes, and vertical asymptotes alike and different?

●Why are all solutions generated algebraically not necessarily solutions to the original equation? How
can we identify these extra solutions?

●Why is it important to set a rational inequality to 0 before solving?

Vocabulary

asymptote, end behavior, extraneous solution, holes, horizontal asymptote, intercepts, least common
denominator, least common multiple, rational function, reciprocal, slant asymptote, vertical asympotes, zeros

Opening 1

Video on Adding and Subtracting Rational Expressions

I will work on problem #9

Worksheet

Group Work Continuous Compound Interest

Must do the problem for the level that you choose:

Beginning: Do the following problem: 17

Intermediate: Do the following problem: 20

Advanced : Do the following problem: 21

Worksheet

Closing on solving growth and decay

Example on white board

Take Notes

5 minutes - take notes for your future forgetful self along with any key vocabulary.

Check your understanding problems

Try any of the other problems listed in the Worksheet and advise me should you
have any questions.

Poll

How comfortable do you feel with adding and subtracting rational expressions?

• I got this!

• I pretty much have this.

• Ok but still have questions.

• I feel lost.