Types of Graphs of Functions

Analyzing Functions and Graphs

By Courtney Kay

Linear vs. Nonlinear

• Linear functions shows a constant rate of change.

• Nonlinear functions do not have a constant rate of change.

Compare Linear and Nonlinear Functions

From a Graph

• When graphed, a linear function forms a single straight line.

• When graphed, a nonlinear function does not form a single straight line.

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Distance - Time graphs

• A horizontal line means stationary.

• A straight line means constant speed.

• If the gradient increases the object is speeding up (accelerating).

• If the gradient decreases the object is slowing down (decelerating).

• If the line is going down, the object is moving backwards.

If DISTANCE is on the y-axis.....

• You're looking at HOW FAR something has moved over time

• It will show you how fast something has moved

When you analyze the graph, you will notice that Leroy's path was faster than the other two runners.

Delivery Driver

A delivery driver's work day is shown in the graph. Each section represents 1 hour of his work day. As time is passing, he is increasing, decreasing or remaining constant from his distance to the warehouse where he works. Use this image to answer the questions in this lesson.

Multiple Choice

What is occuring in section 1?

• Staying still

• Slowly Increasing

• Traveling at a constant rate

• Quickly increasing

Multiple Choice

What is occurring in section 2?

• Staying still

• Travelling Faster than Section 1

• Travelling slower than Section 1

• Returning to warehouse

Multiple Choice

What is occurring in section 3?

• Staying still

• Returning to the warehouse

• Increasing speed

• Decreasing speed

Multiple Choice

What is occurring in section 4?

• Staying still

• Travelling at a constant speed

• Increasing speed

• Decreasing speed

Multiple Choice

What is occurring in section 5?

• Staying still

• Increasing speed

• Decreasing speed

• Travelling at a constant rate

Multiple Choice

What is occurring in section 6?

• Decreasing speed

• Increasing speed

• Staying Still

• Travelling at a constant rate

Multiple Choice

What is occurring in section 7?

• Staying still

• Increasing Speed

• Decreasing Speed

• Travelling at a constant rate

Multiple Choice

What is occurring in section 8?

• Staying Still

• Increasing Speed

• Decreasing Speed

• Travelling back to warehouse

Multiple Choice

What is occurring in section 9?

• Staying still

• Decreasing speed

• Travelling at a constant Rate

• Increasing Speed

Multiple Choice

Match the description to the graph:

"The car is slowing down."

Multiple Select

Match the description to the graph:

"The car is traveling at a constant speed."

Multiple Choice

Match the description to the graph:

"The car is coming back."

Multiple Choice

What does this graph represent?

• Constant speed
• Acceleration
• Not moving

Multiple Choice

At 60 seconds, how far had this object traveled? 

• 0 m
• 10 m
• 20 m
• 40 m

Multiple Choice

How long did it take this object to travel 10 m?

• 0 s

• 10 s

• 15 s

• 20 s

Multiple Choice

On a distance vs. time graph, the steeper the slope _____

• the slower the speed
• the faster the speed
• less acceleration
• greater acceleration

Multiple Choice

Which function has the GREATEST rate of change?

Multiple Choice

How far was Edward from home when he visited Nicola?

• 20 MILES

• 30 MILES

• 40 MILES

Multiple Choice

HOW LONG DID EDWARD STOP FOR?

• 1 HOUR AND 30 MINUTES

• 2 HOURS

• 2 HOURS AND 30 MINUTES