IF.4: PARENT FUNCTIONS AND THEIR CHARACTERISTICS

October 20th, 2014

Vocabulary

Domain: The value that is the ________in a function or relation. Range: The set of all possible _________ of a function. x-intercept: The point where a line meets or crosses the _______

y-intercept: The point where a line meets or crosses the _______ Interval of Increasing: the domain (x-values) over which a

function is ______________ Interval of Decreasing: the domain (x-values) over which a

function is ______________

x-axis

y-axis

increasing

decreasing

inputs

outputs

Vocabulary

Minimum: the ____________ point on a graph Maximum: the ____________ point on a graph Rate of Change: the rate at which a function is ______________

or ______________ (constant) How do you tell if a graph is positive? ________ the x-axis How do you tell if a graph is negative? _______ the x-axis

above

below

increasingdecreasing

lowest

highest

Example 1: Consider the graph . Identify the following properties for the graph of the function .

Domain: all real numbers Range: y > 0 x-intercept: None y-intercept: (0, 1) Interval of Increasing: all real #s or Interval of Decreasing: None Minimum or Minimum: None Positive: all real numbers Negative: never

Example 2: Consider the function f(x) = x. Graph the functions below.

x y

-2 -2

-1 -1

0 0

1 1

2 2

This is known as the parent function of a linear equation.

Identify the following properties for the graph of the function f(x) = x. x y

-2 -2

-1 -1

0 0

1 1

2 2

Interval of Increasing: as x increases, f(x) increases

Interval of Decreasing: as x decreases, f(x) decreases

Minimum or Minimum: NonePositive: x > 0Negative: x < 0

Domain: all real numbers

Range: all real numbers

x-intercept: (0, 0)

y-intercept: (0, 0)

Example 3: Consider the function f(x) = -x. Graph the functions below.

x y

-2 2

-1 1

0 0

1 -1

2 -2

Interval of Increasing: as x increases, f(x) decreases

Interval of Decreasing: as x decreases, f(x) increases

Minimum or Minimum: NonePositive: x < 0Negative: x > 0

Domain: all real numbers

Range: all real numbers

x-intercept: (0, 0)

y-intercept: (0, 0)

Example 4: A company uses the function to represent the depreciation of a truck, where V is the value of the truck and x is the number of years after its purchase. Use the table of values shown below.

What is the y-intercept of the graph of the function?From the table, when x = 0, V(x) = 28,000. So, (0, 28000)

Does the graph of the function have an x-intercept? There is not one on the table, but could we find one? YES!For the x-intercept, V(x) = 0, so:

Does the function increase or decrease? Decrease Why?