1-3 TRANSFORMING LINEAR FUNCTIONS CHAPTER 1. WARM UP.

1 - 3 T RA N S F O R M I N G L I N E A R F U N C T I O N S

CHAPTER 1

WARM UP

Instructions: Name the parent function of the following problems:1.

2.

3.

4.

WARM UP ANSWER

Instructions: Name the parent function of the following problems:1.Answer: Quadratic Function 2. Answer: Rational Function3. Answer: Linear function4. Answer; Square root function

OBJECTIVES

• The student will be able to:• Transform linear functions• Solve problems involving linear transformations

TRANSFORMING LINEAR FUNCTIONS

• What is a transformation?• Answer: A transformation is a change in the position,

size, or shape of a figure or graph.

• What is a Linear function?• Answer: is a function, meaning we have an input and

an output, that can be written in the form . Its graph is a line.

• If we transforming linear functions , we can say we are changing the linear function either the way it looks in the graph or the equation.


• There are four ways we can transform the linear function by :• Just remember the x changes


Just remember y changes


Just remember y is the mirror so the one that changes is the x


Just remember x is the mirror so the one that changes is the y

EXAMPLE 1

• Let g(x) be the indicated transformation of f(x).Write the rule for g(x).• ; g(x) is a horizontal shift 3 units to the right.• Solution: • subtract 3 from the input• evaluate f at x-3• Simplify

EXAMPLE 2

• Let g(x) be the indicated transformation of f(x).Write the rule for g(x).• ; g(x) is reflected about the y-axis.• Solution: • change the input of f• Simplify•

STUDENT PRACTICEEXAMPLE 3

• Let g(x) be the indicated transformation of f(x).Write the rule for g(x).• ; g(x) is a vertical shift (vertical translation) 3

units down.


• Let g(x) be the indicated transformation of f(x).Write the rule for g(x).• ; g(x) is a reflection across the x-axis.

LETS COMBINE TRANSFORMATIONSEXAMPLE 5

• Let g(x) be the indicated transformation of f(x).Write the rule for g(x).• ; g(x) is a vertical shift (vertical translation) 3

units down followed by a reflection across the x-axis• .Solution:• First lets take care of the vertical translation

• substitute• simplify

EXAMPLE 5 CONTINUE

• Then we continue with the reflection across the x-axis

STRETCHES AND COMPRESSION

• Stretches and compressions change the slope of a linear function. If the line becomes steeper, the function has been stretched vertically or compressed• horizontally. If the line becomes flatter, the

function has been compressed vertically or stretched horizontally.

STRETCHES AND COMPRESSIONS

EXAMPLE 6

• Let g(x) be a vertical compression of f(x) = 3x + 2 by a factor of 4 . Write the rule for g(x) and graph the function.• Solution:• Vertically compressing f(x) by a factor of

replaces each f(x) with a · f(x) where a = 4 .



• Let g(x) be a horizontal compression of f(x) = 5x - 2 by a factor of 1/3 . Write the rule for g(x) and graph the function.

NOW LETS PUT EVERYTHING TOGETHER

Example 8:Let g(x) be a horizontal compression of f(x) = 6x - 5by a factor of 1/3 followed by a vertical translation 4 units up . Lets h(x) be the horizontal compression and g(x) the vertical translation. Write the rule for g(x) and graph the function.

EXAMPLE 8 CONTINUE

• Now lets take care of the translation


STUDENT PRACTICE

• Do all worksheet•

HOMEWORK

• Page 28 from book• problems 2 to 6 and 12 to14.

CLOSURE

• Today we talked about transforming linear functions through translating and reflecting . • Tomorrow we are going to see scatter plots and

the best fit line.

HAVE A GREAT DAY!!!

1-3 TRANSFORMING LINEAR FUNCTIONS CHAPTER 1. WARM UP.

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