Lesson 1 6 Basic Functions and Function Transformations

Lesson 1. 6: Basic Functions and Function Transformations

Graphs of Common Functions • Seven functions that are frequently encountered in algebra are: • It is essential to know the characteristics of the graphs of these functions. • These are called “parent functions”

Graphs of Common Functions (continued) • • • is known as the constant function. The domain of this function is: The range of this function is: The function is constant on C This function is even.

Graphs of Common Functions (continued) • is known as the identity function. • The domain of this function is: • The range of this function is: • The function is increasing on • This function is odd.

Graphs of Common Functions (continued) • • • is the absolute value function. The domain of this function is: The range of this function is: The function is decreasing on and increasing on This function is even.

Graphs of Common Functions (continued) • is the standard quadratic function. • The domain of this function is: • The range of this function is: • The function is decreasing on • and increasing on • This function is even.

Graphs of Common Functions • • • is the square root function. The domain of this function is: The range of this function is: The function is increasing on This function is neither even nor odd.

Graphs of Common Functions (continued) • • • is the standard cubic function. The domain of this function is: The range of this function is: The function is increasing on This function is odd.

Graphs of Common Functions (continued) • • • is the cube root function. The domain of this function is: The range of this function is: The function is increasing on This function is odd.

Graphs of Common Functions (continued) Equation What happens to y or x ? Type of Transformation

Vertical Shifts

Horizontal Shifts

Vertically Stretching and Shrinking Graphs

Horizontally Stretching and Shrinking Graphs

Ex 1: Ex 2: Ex 3: Ex 4: Ex 5:

Ex 6:

HW: • pg 226 1 -13 eoo, 45 -117 eoo • Web. Work