Exploring Function Basics and Notation

The video provides a comprehensive review of functions, including their notation and properties. It explains the concept of functions as mathematical objects that map inputs to unique outputs, using a vending machine analogy. The video covers function notation, graph analysis, and properties such as increasing, decreasing, local maximums, and minimums. It also discusses intercepts on graphs, providing examples and practice questions to reinforce understanding.

What is the typical notation used for the input and output of a function?

• A for input, B for output

• X for input, Y for output

• M for input, N for output

• P for input, Q for output

Which analogy is used to explain the unique output property of functions?

• A vending machine

• A washing machine

• A computer

• A calculator

What test is often used to determine if something is a function?

• Diagonal line test

• Vertical line test

• Horizontal line test

• Curved line test

If f(0) = 3, what is the corresponding coordinate point?

• (3, 0)

• (0, 3)

• (0, -3)

• (-3, 0)

For which x-value is f(x) equal to -1?

• x = -4

• x = 4

• x = -1

• x = 0

What does it mean for a graph to be increasing?

• The graph is going downhill

• The graph is flat

• The graph is going uphill

• The graph is curving

At which x-value does the graph change from decreasing to increasing?

• x = -1

• x = 3

• x = -3

• x = 0

What is a local maximum?

• A peak in a small section of the graph

• A valley in a small section of the graph

• The highest point on the entire graph

• The lowest point on the entire graph

Where does the function touch or cross the horizontal axis?

• At the origin

• At the horizontal intercept

• At the vertical intercept

• At the maximum point

What is the vertical intercept of the function in the example?

• (0, -3)

• (3.5, 0)

• (3, 0)

• (0, 3)