Algebra II Unit 8

Big Idea:

Examining and understanding properties of exponential and logarithms; Graphs and transformations of exponential and logarithms

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.5(A) determine the effects on the key attributes on the graphs of f(x) = b^x and f(x) = log_b (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d

2A.5(C) rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations

2A.8(C) predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models

Focus TEKS

2A.8(A) analyze data to select the appropriate model from among linear, quadratic, and exponential models

2A.8(B) use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data

Ongoing TEKS

2A.7(I) [Supporting] write the domain and range of a function in interval notation, inequalities, and set notation

Student Learning Targets:

• I will identify data that grows exponentially
• I will compare the rates of change of linear and exponential data
• I will identify and write exponential functions
• I will determine the decay factor or growth factor of an exponential function
• I will determine when an exponential function is increasing or decreasing
• I will describe the end behavior of exponential functions
• I will identify the asymptotes of exponential functions
• I will graph transformations of exponential functions
• I will graph (x) = e^x and graph transformations of that function
• I will find the domain and range of an exponential function
• I will rewrite exponential equations as their corresponding logarithmic equations
• I will rewrite logarithmic equations as their corresponding exponential equations
• I will make conjectures about properties of logarithms
• I will apply the Product Property and Quotient Property of Logarithms
• I will rewrite logarithmic expressions by using properties
• I will write and apply the Power Property of Logarithms

Essential Questions:

• What characterizes exponential growth and decay?
• How can one differentiate an exponential model from a linear model given a real world set of data?

Extra Information:

Adopted Textbook: Springboard - Algebra II Texas Edition

District Grading Policy

Texas Gateway Online Resource Center