Linear Functions and Their Properties

The video tutorial covers lessons 6.1 and 6.2a on relations and functions. It begins with an introduction to the concept of functions, defining them as relationships with one output for each input. The teacher provides examples of linear functions, such as y = 2x + 6, and non-functions, like y = sqrt(x), to illustrate the difference. The tutorial also includes exercises on solving for outputs given inputs and vice versa using the equation y = -3x + 2. The video emphasizes understanding the input-output relationship and the importance of function notation.

What is a function in mathematical terms?

• A relationship with only inputs

• A relationship with no outputs

• A relationship with one output for each input

• A relationship with multiple outputs for each input

In the context of functions, what does the term 'input' usually refer to?

• The variable y

• The slope

• The constant term

• The variable x

In the equation y = 2x + 6, what is the output when the input is 1?

• 4

• 8

• 6

• 10

What is the main characteristic of a linear function?

• It has multiple outputs for each input

• It is always a quadratic equation

• It has a constant rate of change

• It has no inputs

Why is y = √x not considered a function?

• It has multiple outputs for a single input

• It has no inputs

• It has no outputs

• It is a linear equation

Can multiple inputs have the same output in a function?

• No, inputs and outputs must always be unique

• Yes, but only if the outputs are different

• No, each input must have a different output

• Yes, as long as each input has a unique output

What is the output of the function y = -3x + 2 when x = -3?

• 11

• -11

• 9

• -9

If y = -3x + 2 and y = 10, what is the value of x?

• 10/3

• -10/3

• 8/3

• -8/3

What happens when you substitute x = 5 into the equation y = -3x + 2?

• y = -11

• y = -15

• y = -17

• y = -13

What is the first step in solving for x when given y in the equation y = -3x + 2?

• Divide both sides by -3

• Multiply both sides by 3

• Subtract 2 from both sides

• Add 2 to both sides