Analyzing the Domain and Range of Quadratic Functions through Graphs

This lesson teaches how to determine the domain and range of a quadratic function by analyzing its graph. The domain is the set of all possible x-values, while the range is the set of all possible y-values. By examining the graph, one can trace the x-values along the x-axis and the y-values along the y-axis to identify the domain and range. The lesson explains that the domain often includes all real numbers, while the range is determined by the minimum and maximum y-values the graph reaches. Practical examples with parabolas are used to illustrate these concepts.

What is the domain of a quadratic function when looking at its graph?

• All real numbers

• All negative integers

• Only whole numbers

• All positive integers

How can you determine the range of a quadratic function from its graph?

• By checking the symmetry of the graph

• By counting the number of peaks

• By identifying the lowest and highest y-values

• By looking at the x-axis

If a parabola has a lowest point at y = 2, what is the range?

• y is between 0 and 2

• y is equal to 2

• y is greater than or equal to 2

• y is less than or equal to 2

What does it mean if a quadratic graph continues indefinitely in both directions along the x-axis?

• The domain includes all real numbers

• The domain includes only positive numbers

• The domain is limited to a specific range

• The domain is undefined

In the context of a quadratic graph, what does 'y is less than or equal to -2' signify?

• The graph never reaches y = -2

• The highest point on the graph is y = -2

• The graph only includes positive y-values

• The graph is symmetrical around y = -2