Key Features of Functions in Algebra 2

This lesson covers key features of functions, focusing on domain and range, positive and negative intervals, increasing and decreasing intervals, and the average rate of change. It explains how to interpret graphs and equations to understand relationships between quantities, using examples and graphing tools like Desmos.

What is the main focus of lesson 1-1?

• Reading and understanding graphs

• Creating graphs

• Memorizing formulas

• Solving equations

Which tool is recommended for graphing equations in this lesson?

• Microsoft Excel

• Google Sheets

• Desmos

• Wolfram Alpha

What does the domain of a function represent?

• The lowest x-value

• The highest y-value

• All possible x-values

• All possible y-values

How is the domain of the function y = x^2 - 3 represented in interval notation?

• (-3, ∞)

• (-∞, 3)

• (-3, 3)

• (-∞, ∞)

What is the range of the function y = x^2 - 3 in set builder notation?

• y > -3

• y < -3

• y ≥ -3

• y ≤ -3

In which intervals is the function y = x^2 - 9 positive?

• (-∞, -3) and (3, ∞)

• (-3, 3)

• (-∞, 3)

• (3, ∞)

What does it mean when a graph is decreasing?

• The x-values are increasing

• The y-values are increasing

• The y-values are decreasing

• The x-values are decreasing

Over which interval is the function y = x^2 decreasing?

• (-∞, ∞)

• (-∞, 0)

• (0, 1)

• (0, ∞)

What is the formula for the average rate of change?

• (f(a) - f(b)) / (a - b)

• (f(b) - f(a)) / (b - a)

• (f(a) + f(b)) / (a + b)

• (f(b) + f(a)) / (b + a)

What does a different average rate of change between intervals indicate about a function?

• The function is constant

• The function is not linear

• The function is quadratic

• The function is linear