Characteristics and Tests of Functions

The video tutorial introduces the concept of functions, explaining what they are and how to identify them visually. It covers drawing linear functions and parabolas, highlighting key features like gradients and intercepts. The tutorial also demonstrates how to use the vertical line test to distinguish functions from non-functions. The session concludes with a brief mention of more advanced topics like trigonometry and multiple outputs.

What is a simple method to determine if a relation is a function?

• Using complex equations

• Memorizing definitions

• Calculating derivatives

• Drawing graphs

What does the number '2' represent in the equation y = 2x - 3?

• The y-intercept

• The x-intercept

• The gradient

• The vertex

What does the y-intercept of a line tell us?

• The steepness of the line

• The slope of the line

• Where the line crosses the x-axis

• Where the line crosses the y-axis

What is the shape of the graph for the equation y = x^2?

• A hyperbola

• A parabola

• A circle

• A straight line

What happens when you swap the x and y axes in a graph?

• The graph becomes a straight line

• The graph becomes a sideways parabola

• The graph becomes a circle

• The graph remains unchanged

What is the center of the unit circle?

• At (1,1)

• At (0,1)

• At the origin

• At (1,0)

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

• Horizontal line test

• Curved line test

• Diagonal line test

• Vertical line test

What is the main characteristic of a function in terms of inputs and outputs?

• Each input has multiple outputs

• Each input has exactly one output

• Each output has multiple inputs

• Each output has exactly one input

What is the radius of the unit circle?

• Two

• Zero

• One

• Three

What happens when a vertical line intersects a graph at more than one point?

• The graph is a straight line

• The graph is a circle

• The graph is not a function

• The graph is a function