Understanding Linear and Exponential Functions

The video tutorial explains how to identify linear, quadratic, and exponential functions using ordered pairs. Linear functions are characterized by a constant change in y for a constant change in x, while quadratic functions show a pattern of consecutive odd numbers. Exponential functions are identified by consistent multiplication ratios. The tutorial emphasizes the importance of checking calculations thoroughly to avoid errors.

What is the primary focus when identifying different types of functions from ordered pairs?

• The type of numbers used

• The color of the graph

• The pattern of changes in Y

• The size of the numbers

What characterizes a linear function in terms of changes in Y?

• Y changes by decreasing amounts

• Y changes by increasing amounts

• Y changes randomly

• Y changes by a constant amount for each unit change in X

If the differences in Y values are not constant, what can be concluded about the function?

• It is undefined

• It is exponential

• It is not linear

• It is definitely linear

What happens to the Y values in a linear function as X increases by one?

• Y values increase exponentially

• Y values decrease randomly

• Y values increase or decrease by a constant slope

• Y values remain constant

What is a key indicator of a quadratic function?

• Random changes in Y

• Changes in consecutive odd numbers

• Constant ratios in Y

• Constant differences in Y

How do perfect squares relate to quadratic functions?

• They are unrelated

• They indicate exponential growth

• They show changes in consecutive odd numbers

• They indicate linear growth

What effect does a leading coefficient have on a quadratic function?

• It changes the color of the graph

• It has no effect

• It affects the pattern of changes

• It makes the function linear

In a quadratic function, what happens to the differences between consecutive Y values?

• They increase exponentially

• They decrease linearly

• They form a pattern of consecutive odd numbers

• They remain constant

What is the primary method to identify an exponential function?

• Observing random changes

• Using ratios and multiplication

• Looking for changes in consecutive odd numbers

• Checking for constant differences

What is the base in an exponential function if the sequence is 4, 12, 36, 108?

• 3

• 4

• 2

• 5