Domain and Range Questions

This section focuses on domain and range concepts and introduces rules for working with exponents.

The page begins with questions about identifying domain and range in various function representations, including graphs and tables. It emphasizes the importance of understanding these concepts in relation to functions.

Example: A graph is shown, asking students to determine if it represents a function and identify its domain and range.

The section then transitions to rules of exponents, covering several key concepts:

Vocabulary: Product Rule - When multiplying terms with the same base, add the exponents (x^a * x^b = x^(a+b)) Vocabulary: Quotient Rule - When dividing terms with the same base, subtract the exponents (x^a / x^b = x^(a-b)) Vocabulary: Power Rule - When raising a power to another power, multiply the exponents ((x^a)^b = x^(ab)) Vocabulary: Zero Rule - Any number (except 0) raised to the power of 0 equals 1 (a^0 = 1, where a ≠ 0) Vocabulary: Negative Rule - For negative exponents, the base can be moved to the denominator with a positive exponent (x^-a = 1/x^a)

The page also introduces the concepts of x-intercept and y-intercept:

Definition: X-intercept - the point where a line or curve crosses the x-axis Definition: Y-intercept - the point where a line or curve crosses the y-axis

Highlight: The page reminds students of the order of operations: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right)

Growth of Patterns

This section explores how patterns grow and introduces different types of functions.

The page introduces inverse variation and direct variation functions. It explains that inverse variation is represented by the equation y = k/x, where k is a constant, and results in a decreasing pattern. Direct variation, on the other hand, shows a proportional relationship between y and x.

Example: For inverse variation, y = -15/x is given as an example.

The concept of exponential functions is also introduced, represented by the equation y = ab^x + k, where a is the initial value and b is the multiplier. This type of function results in an increasing pattern.

Highlight: The page emphasizes that a function can have repeating y values, but each input value must have only one output value to be considered a function.

Vocabulary: Domain - the set of input values (x) for a function Vocabulary: Range - the set of output values (y) for a function

The page includes several practice problems covering various function types and asks students to determine domain and range.