Interpreting Graphs: Key Concepts and Techniques

Mr. Backer introduces graphing skills, focusing on recognizing reasonable graphs, identifying key characteristics like domain and range, and understanding graphing technology limitations. He provides examples using the square root function y = sqrt(4 - x^2) and the power function y = x^(2/3), explaining how to determine domain and range for each.

What is one of the key skills needed to interpret graphs effectively?

• Understanding the color scheme of the graph

• Recognizing if a graph is reasonable

• Knowing the history of graphing

• Memorizing all graph equations

What does the term 'parent functions' refer to?

• Functions that are always linear

• Functions that are only used in calculus

• Functions that are not graphable

• The original functions from which other functions are derived

Which of the following is an important characteristic of a graph?

• The domain and range

• The type of paper used for graphing

• The color of the graph

• The speed of graphing

What should you do if your graphing technology shows something that seems incorrect?

• Assume it is correct

• Ignore it

• Verify the graph manually

• Change the graphing tool

What is the domain of the function y = sqrt(4 - x^2)?

• (-∞, ∞)

• [-2, 2]

• (-2, 2)

• [0, 4]

What is the range of the function y = sqrt(4 - x^2)?

• [-2, 2]

• (-∞, ∞)

• [0, 2]

• [0, 4]

What does the range of a function refer to?

• The x-values of the graph

• The y-values of the graph

• The intercepts of the graph

• The slope of the graph

What should you do if the graph does not extend to the x-axis?

• Ignore the graph

• Check the function to verify the end values

• Assume the graph is incorrect

• Change the graphing tool

What is the domain of the function y = x^(2/3)?

• [-1, 1]

• (-∞, 0]

• [0, ∞)

• (-∞, ∞)

What is the range of the function y = x^(2/3)?

• (-∞, ∞)

• [0, ∞)

• [-1, 1]

• [0, 2]