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