Understanding Functions and Graphs

The video tutorial explains algebraic functions, starting with a simple equation y = x + 1. It covers how to create a function table and graph these functions on a coordinate plane. The tutorial introduces different types of functions, such as linear, quadratic, and trigonometric, and explains how to identify them using the vertical line test. An example of a non-function graph, y squared = x, is provided to illustrate when a graph does not pass the vertical line test.

What is the output value when the input value is -2 in the equation y = x + 1?

• 2

• 0

• -1

• 1

How can ordered pairs be used in graphing functions?

• They determine the color of the graph.

• They indicate the type of function.

• They are used to plot points on the coordinate plane.

• They represent the slope of the graph.

What type of function is represented by a straight line on a graph?

• Quadratic function

• Cubic function

• Linear function

• Trigonometric function

Which of the following is NOT a type of function mentioned in the video?

• Trigonometric function

• Cubic function

• Exponential function

• Quadratic function

What does the vertical line test help determine about a graph?

• The slope of the graph

• The symmetry of the graph

• Whether the graph represents a function

• The color of the graph

What is the key condition for a graph to pass the vertical line test?

• The graph must be below the x-axis.

• The graph must be above the x-axis.

• The graph must intersect the vertical line at exactly one point for each x value.

• The graph must be a straight line.

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

• The graph is a quadratic function.

• The graph is a linear function.

• The graph does not represent a function.

• The graph represents a function.

Which equation is used as an example of a graph that fails the vertical line test?

• y^2 = x

• y = sin(x)

• y = x^2

• y = x + 1

Why does the graph of y^2 = x fail the vertical line test?

• It is a straight line.

• It is a quadratic function.

• It intersects the vertical line at multiple points for some x values.

• It has no intersection with the vertical line.

What is the implication of a graph failing the vertical line test?

• The graph is a linear function.

• The graph is not a function.

• The graph is a function.

• The graph is a trigonometric function.