#### Type:

Graphic Organizer/Worksheet

#### Description:

In this lesson we focus on vertical translations of graphs of linear and exponential functions. We relate the vertical translation of a linear function to its y-intercept. This lesson is based upon the common core standard, 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. We experiment with cases and illustrate an explanation of the effects on the graph using technology.

#### Subjects:

• Mathematics > Algebra
• Mathematics > General

#### Keywords:

reason quantitatively solve equations number relationships process of reasoning inequalities variable

English

#### Access Privileges:

Public - Available to anyone

#### Collections:

None
Update Standards?

#### CCSS.Math.Content.HSF-IF.A.1: Common Core State Standards for Mathematics

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

#### CCSS.Math.Content.HSF-IF.A.2: Common Core State Standards for Mathematics

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

#### CCSS.Math.Content.HSF-IF.A.3: Common Core State Standards for Mathematics

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

#### CCSS.Math.Content.HSF-IF.C.7a: Common Core State Standards for Mathematics

Graph linear and quadratic functions and show intercepts, maxima, and minima.

#### CCSS.Math.Content.HSF-IF.C.7b: Common Core State Standards for Mathematics

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

#### CCSS.Math.Content.HSF-IF.C.7c: Common Core State Standards for Mathematics

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

#### CCSS.Math.Content.HSF-IF.C.7d: Common Core State Standards for Mathematics

(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

#### CCSS.Math.Content.HSF-IF.C.7e: Common Core State Standards for Mathematics

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

#### CCSS.Math.Content.HSF-IF.C.9: Common Core State Standards for Mathematics

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### CCSS.Math.Content.HSF-BF.B.3: Common Core State Standards for Mathematics

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.

#### MA.9-12.CCSS.Math.Content.HSF-IF.A.1: Mathematics

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

#### MA.9-12.CCSS.Math.Content.HSF-IF.A.2: Mathematics

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

#### MA.9-12.CCSS.Math.Content.HSF-IF.A.3: Mathematics

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

#### MA.9-12.CCSS.Math.Content.HSF-IF.C.7a: Mathematics

Graph linear and quadratic functions and show intercepts, maxima, and minima.

#### MA.9-12.CCSS.Math.Content.HSF-IF.C.7b: Mathematics

Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

#### MA.9-12.CCSS.Math.Content.HSF-IF.C.7c: Mathematics

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

#### MA.9-12.CCSS.Math.Content.HSF-IF.C.7d: Mathematics

Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

#### MA.9-12.CCSS.Math.Content.HSF-IF.C.7e: Mathematics

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

#### MA.9-12.CCSS.Math.Content.HSF-IF.C.9: Mathematics

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

#### MA.9-12.CCSS.Math.Content.HSF-BF.B.3: Mathematics

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.
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