TRANSFORMATIONS OF FUNCTIONS Mr. Velazquez Honors Precalculus
TRANSFORMATIONS OF FUNCTIONS Mr. Velazquez
Honors Precalculus
COMMON GRAPHS IN ALGEBRA
COMMON GRAPHS IN ALGEBRA
COMMON GRAPHS IN ALGEBRA
COMMON GRAPHS IN ALGEBRAReciprocal Function
• Domain: −∞, 0 ∪ 0,∞• Range: −∞, 0 ∪ 0,∞• Decreasing on −∞, 0 ∪ 0,∞• Odd function
𝑓 𝑥 =1
𝑥
VERTICAL SHIFT
VERTICAL SHIFT
VERTICAL SHIFT
Now, use the graph of f(x)=|x| to obtain g(x)=|x|-2
HORIZONTAL SHIFT
HORIZONTAL SHIFT
HORIZONTAL SHIFT
Use the graph of 𝒇 𝒙 = 𝒙𝟐 to obtain 𝒈 𝒙 = 𝒙 + 𝟏 𝟐
Use the graph of 𝒉 𝒙 = 𝒙 to obtain 𝒋 𝒙 = 𝒙 + 𝟐 − 𝟏.
REFLECTIONS
REFLECTIONS
REFLECTIONS
REFLECTIONSUse the graph of f(x)=x3 to obtain the graph of g(x)= (-x)3.
Use the graph of f(x)= x to graph g(x)=- x
VERTICAL STRETCHING AND SHRINKING
VERTICAL STRETCHING AND SHRINKING
HORIZONTAL STRETCHING AND SHRINKING
HORIZONTAL STRETCHING AND SHRINKING
HORIZONTAL STRETCHING AND SHRINKING
SEQUENCES OF TRANSFORMATIONS
A function involving more than one transformation can be graphed by performing transformations in the following order:
1.Horizontal shifting
2.Stretching or shrinking
3.Reflecting
4.Vertical shifting
EXAMPLE:
Use transformations of the
graph of 𝑓 𝑥 = 𝑥2 to graph
𝑔 𝑥 = 2 𝑥 + 3 2 − 1
SEQUENCES OF TRANSFORMATIONS
− − − −
−
−
−
−
x
y
1Given the graph of f(x) below, graph ( 1).
2f x −
SEQUENCES OF TRANSFORMATIONS
− − − −
−
−
−
−
x
y
Given the graph of f(x) below, graph - ( 2) 1.f x + −
SEQUENCES OF TRANSFORMATIONS
− − − −
−
−
−
−
x
y
Given the graph of 𝑓 𝑥 below, graph 2𝑓 −𝑥 − 3
CLASSWORK & HOMEWORK
MATH JOURNAL: Summarize what you learned today
CLASSWORK: TRANSFORMATIONS – Perform three different transformations on the function 𝑓 𝑥 = 𝑥2, giving the equation of the function and also the graph of the function
Homework:
Functions HW 3
Math XL