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90 | eUreka Math algebra II StUdy gUIde
F-IF.C.7e Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.★
e. Graph exponential and logarithmic functions, showing intercepts and end behavior,
and trigonometric functions, showing period, midline, and amplitude.
F-BF.A.1a Write a function that describes a relationship between two quantities.★
a. Determine an explicit expression, a recursive process, or steps for calculation from a
context.
F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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.
F-BF.B.4a Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse
and write an expression for the inverse. For example, f(x) = 2x^3 or f(x) = (x + 1)/(x - 1)
for x ≠ 1.
F-LE.A.2 Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
F-LE.A.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d
are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology.
Instructional Days: 7Student Outcomes
Lesson 16: Rational and Irrational Numbers
● (^) Students interpret addition and multiplication of two irrational numbers in the context
of logarithms and find better-and-better decimal approximations of the sum and
product, respectively.
● (^) Students work with and interpret logarithms with irrational values in preparation for
graphing logarithmic functions.
Lesson 17: Graphing the Logarithm Function
● (^) Students graph the functions fx()=log()x, gx()=log 2 ()x, and hx()=ln()x by hand and
identify key features of the graphs of logarithmic functions.
Lesson 18: Graphs of Exponential Functions and Logarithmic Functions
● (^) Students compare the graph of an exponential function to the graph of its
corresponding logarithmic function.
● (^) Students note the geometric relationship between the graph of an exponential function
and the graph of its corresponding logarithmic function.
Lesson 19: The Inverse Relationship Between Logarithmic and Exponential Functions
● (^) Students understand that the logarithmic function base b and the exponential function
base b are inverse functions.
Lesson 20: Transformations of the Graphs of Logarithmic and Exponential Functions
● (^) Students study transformations of the graphs of logarithmic functions and learn the
standard form of generalized logarithmic and exponential functions.
● (^) Students use the properties of logarithms and exponents to produce equivalent forms
of exponential and logarithmic expressions. In particular, they notice that different
types of transformations can produce the same graph due to these properties.
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