Understanding Functions

The video tutorial introduces the concept of functions, explaining their definition as a special relationship between inputs and outputs. It covers how to create function tables and use the vertical line test to determine if a graph represents a function. Various types of functions, including linear, quadratic, cubic, and more, are discussed. The tutorial also demonstrates how to evaluate both single and multivariable functions.

What is a function primarily described as?

• A random set of numbers

• A collection of unrelated data

• A method for solving equations

• A special kind of relationship between inputs and outputs

What must be true for a relation to be considered a function?

• It must have the same input and output

• It must have multiple outputs for each input

• It must have a single output for each input

• It must have no outputs

In a function table, what indicates that a table is not a function?

• All x values are different

• Same y value for different x values

• All y values are the same

• Common x value leading to different y values

What is the vertical line test used for?

• Calculating the range of a function

• Checking if a graph represents a function

• Determining the slope of a line

• Finding the domain of a function

Which graph passes the vertical line test?

• A graph that touches a vertical line at two points

• A graph that touches a vertical line at one point

• A graph that touches a vertical line at three points

• A graph that does not touch any vertical line

What is the parent function of a quadratic function?

• y = x^3

• y = x^2

• y = √x

• y = x

Which of the following is an example of a linear function?

• y = log x

• y = √x

• y = 3x + 7

• y = x^2 + 4

What type of function is y = e^x?

• Quadratic function

• Logarithmic function

• Linear function

• Exponential function

Which function is characterized by repeating patterns?

• Rational function

• Trigonometric function

• Polynomial function

• Exponential function

What is a characteristic of a rational function?

• The degree of the numerator is greater than the denominator

• The degree of the denominator is greater than the numerator

• It has no variables

• It is always a straight line