Exploring Functions and Their Descriptions

The video tutorial explains the concept of functions, focusing on distinguishing between linear and nonlinear functions. It covers methods such as graph analysis, the vertical line test, and examining constant rates of change. The tutorial also discusses how to determine linearity by analyzing equations and concludes with a summary of the key points.

What is a function in mathematical terms?

• A relation where each input has exactly one output

• A relation where each input can have multiple outputs

• A relation where outputs are always greater than inputs

• A relation where inputs are always greater than outputs

How can you determine if a function is linear by looking at its graph?

• If the graph forms a parabola

• If the graph forms a circle

• If the graph forms a line

• If the graph forms a curve

What does the vertical line test help you determine?

• If a graph is nonlinear

• If a graph is proportional

• If a graph is linear

• If a graph is a function

What indicates a constant rate of change in a table of values?

• The values of Y and X are both constant

• The ratio of change in Y to change in X is constant

• The values of X decrease by different amounts

• The values of Y increase by different amounts

If the ratio of change in Y to change in X is not constant, what type of function is it?

• Linear

• Nonlinear

• Non-proportional

• Proportional

How can you identify a linear function from its equation?

• If it includes a variable in the denominator

• If it includes a cubic term

• If it includes a squared term

• If it can be written in the form y = mx + b

Which of the following equations represents a linear function?

• y = 3x^2 + 2

• y = 4/x + 1

• y = 5x + 3

• y = x^3 - 2x

What is the slope-intercept form of a linear equation?

• y = a/x + b

• y = ax^3 + bx^2 + cx + d

• y = mx + b

• y = ax^2 + bx + c

Which of the following is NOT a characteristic of a linear function?

• It can be written in the form y = mx + b

• It includes a variable raised to a power greater than one

• Its graph is a straight line

• It has a constant rate of change

What does it mean if a graph passes the vertical line test?

• The graph is nonlinear

• The graph is proportional

• The graph is linear

• The graph represents a function