1-3 TRANSFORMING LINEAR FUNCTIONS CHAPTER 1. WARM UP.
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Transcript of 1-3 TRANSFORMING LINEAR FUNCTIONS CHAPTER 1. WARM UP.
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.
TRANSFORMING LINEAR FUNCTIONS
• There are four ways we can transform the linear function by :• Just remember the x changes
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.
STUDENT PRACTICEEXAMPLE 4
• 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
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.
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 .
• substitute• simplify
STUDENT PRACTICEEXAMPLE 7
• 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.
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.