Understanding Functions and Graphs

The video tutorial covers the basics of functions, including their definition, notation, and the concepts of domain and range. It explains how to determine if a relation is a function using the vertical line test and provides practice problems to reinforce understanding. The tutorial also introduces function notation and demonstrates how to evaluate functions with specific inputs.

What defines a function in terms of x and y values?

• Each x-value maps to multiple y-values.

• Each y-value maps to multiple x-values.

• Each x-value maps to exactly one y-value.

• Each y-value maps to exactly one x-value.

How do you interpret f(3) in function notation?

• Divide f by 3.

• Add 3 to the function.

• Multiply f by 3.

• Plug 3 into the function for x.

What is the domain of a function?

• The range of a function.

• The output values of a function.

• The y-values of a function.

• The x-values of a function.

What does the vertical line test determine?

• If a graph is a non-linear function.

• If a graph represents a function.

• If a graph is a quadratic function.

• If a graph is a linear function.

Which set of ordered pairs represents a function?

• {(1, 2), (1, 3), (2, 4)}

• {(1, 2), (2, 2), (2, 3)}

• {(1, 2), (2, 3), (3, 4)}

• {(1, 2), (2, 3), (1, 4)}

What is the slope in the equation y = 4x + 2?

• 6

• 4

• 8

• 2

Which graph is not a function?

• A graph where a horizontal line intersects it at two points.

• A graph where a horizontal line intersects it at one point.

• A graph where a vertical line intersects it at one point.

• A graph where a vertical line intersects it at two points.

What does a linear equation look like?

• y = ax^3 + bx^2 + cx + d

• y = a/x

• y = ax^2 + bx + c

• y = mx + b

How do you identify a non-linear function from a table?

• The y-values increase by a constant amount.

• The x-values increase by a constant amount.

• The x-values and y-values do not follow a consistent pattern.

• The x-values decrease by a constant amount.

What is the y-intercept in the equation y = 4x + 2?

• 0

• 6

• 4

• 2