Determining the Key Features of Function

Graphs

The Key Features of Function Graphs - Preview Domain and Range x-intercepts and y-intercepts Intervals of increasing, decreasing, and

constant behavior Parent Equations Maxima and Minima

Domain

To find the domain of the graph _____________________ of the graph

Determining Domain - Symbols →

→

Determining Domain1. Start at the origin2.

3. Return to the origin4.

Examples

Domain:Domain:

Example

Domain:

Determining Domain - Infinity

Domain:

Examples

Domain: Domain:

Your Turn: In the purple Precalculus textbooks,

complete problems 3, 7, and find the domain of 9 and 10 on pg. 160

3. 7.

9. 10.

Range

To find the range of the graph _____ _________________of the graph

We also use open and closed circles for the range

Determining Range1. Start at the origin2.

3. Return to the origin4.

Examples

Range: Range:

Examples

Range: Range:

Your Turn: In the purple Precalculus textbooks,

complete problems 4, 8, and find the range of 9 and 10 on pg. 160

4. 8.

9. 10.

X-Intercepts Has many names:

x-intercept Roots Zeros

Examples

x-intercepts: x-intercepts:

Y-Intercepts

y-intercepts: y-intercepts:

Seek and Solve!!!

Types of Function Behavior 3 types:

Increasing Decreasing Constant

When determining the type of behavior, ____________________________________________________________________

Roller Coasters!!!

Fujiyama in Japan

Types of Behavior – Increasing Direct Relationship

Types of Behavior – Constant

Types of Behavior – Decreasing Inverse Relationship

Identifying Intervals of Behavior

Increasing: [0, 4)

The y-values are increasing

when the x-values are between 0 inclusive and 4 exclusive

Identifying Intervals of Behavior Increasing:

Constant:

Decreasing:

x

1

1

y

Identifying Intervals of Behavior, cont. Increasing:

Constant:

Decreasing:-1-3

y

x

Don’t get distracted by the arrows! Even though both of the arrows point “up”, the graph isn’t increasing at both ends of the graph!

Your Turn: Complete problems 1 – 4 on The Key

Features of Function Graphs – Part II handout.

1.

2.

3.

4.

What do you think of when you hear the word parent?

Parent Function Flipbook

Parent Function The most basic form of a type of function Determines the general shape of the

graph

Basic Types of Parent Functions1. Linear2. Absolute Value3. Greatest Integer4. Quadratic

5. Cubic6. Square Root7. Cube Root8. Reciprocal

Identifying Parent Equations From Graphs:

Examples

Your Turn: Complete problems 5 – 12 on The Key

Features of Function Graphs handout

Maximum (Maxima) and Minimum (Minima) Points

Identifying Minimum and Maximum Points

You can have any combination of min and max points

Minimum: Maximum:

Examples

Your Turn: Complete problems 1 – 6 on The Key

Features of Function Graphs – Part III handout.

Reminder: Find f(#) and Find f(x) = x

Find f(#) Find the value of f(x)

when x equals #. Solve for f(x) or y!

Find f(x) = # Find the value

of x when f(x) equals #.

Solve for x!

Evaluating Graphs of Functions – Find f(#)

1.

2.

f(1) = f(–2) =

Evaluating Graphs of Functions – Find f(x) = #

1.

2.

f(x) = –2 f(x) = 2

Example

1. Find f(1)

2. Find f(–0.5)

3. Find f(x) = 0

4. Find f(x) = –5

Your Turn: Complete Parts A – D for problems 7 – 14

on The Key Features of Function Graphs – Part III handout.