Exploring Functions and Function Notation

The video tutorial covers the basics of functions, including independent and dependent variables, domain and range, and function notation. It explains how to determine if a graph represents a function using the vertical line test and provides examples of domain and range in different contexts. The tutorial also discusses special cases that affect domain, such as fractions and square roots, and reviews function notation. Finally, it explores operations with functions, including addition, subtraction, multiplication, and division of functions.

What is the independent variable typically represented by in a graph?

• Z-axis

• W-axis

• Y-axis

• X-axis

In a basic student budget, what is usually the dependent variable?

• Time

• Money

• Distance

• Speed

How is the domain represented in set notation?

• Minimum y value, maximum y value

• Minimum y value < y < maximum y value

• Minimum x value < x < maximum x value

• Minimum x value, maximum x value

What does a parenthesis in interval notation indicate?

• Value is included

• Value is not included

• Value is equal

• Value is greater

What is a function?

• Each y-value has multiple x-values

• Each x-value has one consistent y-value

• Each y-value has one consistent x-value

• Each x-value has multiple y-values

What test can be used to determine if a graph represents a function?

• Horizontal Line Test

• Diagonal Line Test

• Vertical Line Test

• Curved Line Test

What type of numbers cannot be taken under a square root to get a real value?

• Positive numbers

• Zero

• Negative numbers

• Even numbers

What is the domain of the function x^2 + 2?

• All negative numbers

• All positive numbers

• All integers

• All real numbers

What does f + g of x represent?

• f of x minus g of x

• f of x plus g of x

• f of x times g of x

• f of x divided by g of x

What is the result of f times g of x if f(x) = x^2 + 9 and g(x) = 3x + 5?

• 3x^3 + 5x^2 + 27x + 45

• 3x^3 + 5x^2 + 27x + 9

• 3x^3 + 5x^2 + 27x + 5

• 3x^3 + 5x^2 + 9x + 45