Understanding Function Relationships and Linear Equations

The video tutorial explains how to analyze a table representing a function relationship. It guides viewers through determining the output value for a given input and deriving a function rule for the entire table. The tutorial highlights the pattern in inputs and outputs, leading to the formulation of a linear equation in slope-intercept form. The function rule is verified by evaluating it with specific inputs to ensure it matches the corresponding outputs.

What is the domain of the function in the given problem?

• The range of the function

• The set of all possible outputs

• The set of all possible inputs

• The difference between inputs and outputs

If the input increases by 4, what is the corresponding increase in the output?

• 1

• 2

• 3

• 4

What is the value of Z when the input is 8?

• -3

• -1

• 1

• 0

What does a constant ratio of change in Y to change in X indicate?

• A quadratic equation

• A linear equation

• An exponential equation

• A logarithmic equation

What is the slope of the linear equation derived from the table?

• 1/4

• 4

• 1/2

• 2

What is the y-intercept of the linear equation derived from the table?

• -5

• -7

• 0

• 5

How is the linear equation written in function form?

• F(N) = 2N - 5

• F(N) = 1/2N - 5

• F(N) = 1/2N + 5

• F(N) = 2N + 5

What is the first step in writing a function rule from a table?

• Verify the outputs

• Determine the pattern in inputs

• Calculate the slope

• Identify the y-intercept

What is the output when the input is 12 according to the function rule?

• 3

• 2

• 1

• 0

What is the purpose of verifying the function rule with given inputs?

• To find new inputs

• To ensure the outputs match the table

• To change the function rule

• To calculate the domain