Exploring Linear Functions and Rate of Change

What is a function in mathematics?

• A relation where inputs and outputs are the same

• A relation with no specific pattern

• A relation where each input has a unique output

• A relation where each input has multiple outputs

Why are linear functions called 'linear'?

• Because they form a triangle when graphed

• Because they have no specific pattern

• Because they form a circle when graphed

• Because they form a line when graphed

What does the Greek letter delta (Δ) represent in the context of rate of change?

• Product

• Change

• Difference

• Sum

How is the rate of change usually represented?

• As a difference between x and y

• As a fraction of change in y over change in x

• As a product of x and y

• As a sum of x and y

What is the output of the function f(x) = 3x - 2 when the input is -2?

• -4

• 2

• -8

• 4

What ordered pair represents the input -1 for the function f(x) = 3x - 2?

• (-1, -2)

• (-1, 1)

• (-1, -5)

• (-1, -3)

What pattern is observed in the graph of a linear function?

• The points form a triangle

• The points form a circle

• The points are randomly scattered

• The points form a line

How do you find additional points on the graph using the rate of change?

• By moving up and right

• By moving down and right

• By moving down and left

• By moving up and left

What is the solution point when x is 3 for the function f(x) = 3x - 2?

• (3, 6)

• (3, 7)

• (3, 5)

• (3, 8)

How can you tell if a function is linear?

• If its points form a line and it has a constant rate of change

• If its points form a circle

• If it has no specific pattern

• If its points form a triangle