Algebra II Unit 9

Big Idea:

Solving exponential and logarithmic equations. Solving real-world applications of exponential and logarithmic functions.

Student Expectations:

Priority TEKS

2A.2(A) graph the functions f(x)=√x, f(x)=1/x, f(x)=x³, f(x)= ³√x, f(x)=b^x, f(x)=|x|, and f(x)=log_b (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval

2A.2(C) describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range

2A.5(D) solve exponential equations of the form y = ab^x where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions

Focus TEKS

2A.5(B) formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation

2A.5(E) determine the reasonableness of a solution to a logarithmic equation

Student Learning Targets:

• I will use compositions to verify two functions are inverse
• I will define the logarithm of y with base b
• I will write the Inverse Properties of logarithms
• I will apply the properties of logarithms in any base
• I will compare and expand logarithmic expressions
• I will use the Change of Base Formula
• I will find the intercepts and asymptotes of logarithmic functions
• I will determine the domain and range of logarithmic functions
• I will write and graph transformations of logarithmic functions
• I will write exponential equations to represent situations
• I will solve exponential equations
• I will solve exponential equations using logarithms
• I will apply the compounded interest formula
• I will solve logarithmic equations
• I will use properties of logarithms to rewrite logarithmic expressions
• I will solve exponential and logarithmic inequalities

Essential Questions:

• How are expressions involving exponents and logarithms related?
• How do you use the properties of exponents to simplify logarithmic expressions and solve logarithmic equation?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center