Understanding Linear Functions and Graphs

The video tutorial teaches how to identify and write rules for linear functions by recognizing patterns in data. It explains the concept of linear patterns, how to determine if a pattern is linear, and how to write a rule using the slope-intercept form. The tutorial also covers graphing linear functions and understanding domain and range, emphasizing the importance of consistent differences in x and y values for linearity.

What is the pattern in the number of blocks added in each row?

• Add 2 blocks each time

• Add 3 blocks each time

• Add 1 block each time

• Add 4 blocks each time

What is a key characteristic of a linear pattern?

• The differences between consecutive terms are constant

• The differences between consecutive terms are random

• The differences between consecutive terms decrease

• The differences between consecutive terms increase

In a linear function, what must be true about the differences in x and y values?

• All differences in y must be different

• All differences in x and y must be the same

• All differences in x and y must be zero

• All differences in x must be different

What is the formula for a linear function?

• y = mx + b

• y = x^2 + b

• y = mx^2 + b

• y = mx + x

How do you calculate the slope in a linear function?

• Sum of x and y

• Difference of x and y

• Change in y over change in x

• Change in x over change in y

What type of graph is created when plotting a linear function with distinct points?

• Circular graph

• Discrete graph

• Exponential graph

• Continuous graph

What is the domain of a discrete graph of a linear function?

• A set of specific x values

• Only negative numbers

• Only positive numbers

• All real numbers

What is the y-intercept in the function f(x) = 2x - 1?

• 1

• 0

• -1

• 2

What is the slope of the function f(x) = -2x + 1?

• 1

• -2

• -1

• 2

What is the final step in writing a rule for a linear function?

• Identify the slope

• Identify the y-intercept

• Combine the slope and y-intercept into the formula

• Graph the function