Exploring Functions and Relations in Algebra

Lesson 17 covers functions and relations, explaining how functions are special types of relations where each domain value is paired with a unique range value. The lesson discusses the coordinate plane, quadrants, and how to determine if a relation is a function using the vertical line test. Examples are provided to illustrate these concepts, and the lesson concludes with graph analysis to identify domain and range values.

What is a function in the context of mathematics?

• A relation where each value in the range is paired with exactly one value in the domain.

• A graph that intersects the y-axis at multiple points.

• A relation where each value in the domain is paired with exactly one value in the range.

• A set of ordered pairs where the x-values repeat.

Which of the following is true about the coordinate plane?

• The origin is located at the intersection of the x-axis and y-axis.

• It consists of three number lines that intersect perpendicularly.

• Quadrant three contains positive x-values and negative y-values.

• Quadrant one contains negative x-values and positive y-values.

In which quadrant are both x and y values positive?

• Quadrant IV

• Quadrant III

• Quadrant II

• Quadrant I

What does the domain of a function represent?

• All the y-values of a function.

• All the x-values of a function.

• The maximum value of y.

• The minimum value of x.

How can the function y = 2x + 4 be written in function notation?

• 2x + 4 = f(y)

• y = f(x) + 4

• f(y) = 2x + 4

• f(x) = 2x + 4

Which of the following ordered pairs is part of the domain in the example provided?

• (8, 89)

• (1, 76)

• (3, 93)

• (4, 82)

What is the vertical line test used for?

• To find the range of a function.

• To determine if a graph represents a function.

• To identify the x-intercept of a graph.

• To calculate the slope of a line.

If a vertical line intersects a graph at more than one point, what does it indicate?

• The graph represents a function.

• The graph does not represent a function.

• The graph has no x-intercept.

• The graph has no y-intercept.

In the vertical line test, what does it mean if the line touches the graph at only one point?

• The graph has multiple y-values for one x-value.

• The graph is not continuous.

• The graph represents a function.

• The graph does not represent a function.

Which value is not part of the domain in the given graph example?

• 2

• 3.5

• 7

• 8