domain and range worksheet #2 answer key algebra 2

Lemon

2 min read

·

04-02-2025

1

0

Share

Domain and Range Worksheet #2: Answer Key (Algebra 2)

This answer key provides solutions for a hypothetical Algebra 2 worksheet on domain and range. Since the specific questions of your worksheet aren't provided, this key will cover a range of common problem types, demonstrating the methods and principles involved. Remember to always check your work against the original problem statements for accuracy.

Understanding Domain and Range:

Before diving into the answers, let's refresh our understanding of domain and range:

• Domain: The set of all possible input values (usually x-values) for a function. These are the values that make the function defined.
• Range: The set of all possible output values (usually y-values) for a function. These are the values the function can produce.

Types of Problems & Solutions:

Here are examples of common domain and range problems encountered in Algebra 2, along with their solutions:

1. Finding the Domain and Range from a Graph:

(a) Example: Imagine a graph depicting a parabola that opens upwards with a vertex at (2, -1).

• Solution:
  • Domain: Since parabolas extend infinitely to the left and right, the domain is all real numbers, or (-∞, ∞).
  • Range: The parabola's lowest point is at y = -1, and it extends infinitely upwards. Therefore, the range is [-1, ∞).

(b) Example: A graph showing a piecewise function with a discontinuity (a hole or jump).

• Solution: The domain will exclude any x-values where the function is undefined (due to the discontinuity). The range will similarly exclude any y-values not reached by the function. You would specify the domain and range using interval notation, carefully accounting for any excluded values.

2. Finding the Domain and Range from an Equation:

(a) Example: f(x) = √(x - 4)

• Solution:
  • Domain: The square root of a negative number is undefined in the real number system. Therefore, x - 4 ≥ 0, which means x ≥ 4. The domain is [4, ∞).
  • Range: Since the square root is always non-negative, the range is [0, ∞).

(b) Example: g(x) = 1 / (x + 2)

• Solution:
  • Domain: The function is undefined when the denominator is zero, i.e., when x + 2 = 0, or x = -2. The domain is (-∞, -2) U (-2, ∞).
  • Range: The function can take on any value except zero. The range is (-∞, 0) U (0, ∞).

(c) Example: h(x) = x² + 3

• Solution:
  • Domain: This is a quadratic function; the domain is all real numbers, or (-∞, ∞).
  • Range: Since the parabola opens upwards and has a vertex at (0, 3), the minimum value is 3. The range is [3, ∞).

3. Identifying Domain and Range from a Table of Values:

(a) Example: A table showing several (x, y) pairs.

• Solution: Examine the x-values in the table to determine the domain. Then, look at the corresponding y-values to find the range. If the table only provides a sample of points, consider the type of function to infer the complete domain and range. If it's a continuous function, like a polynomial or exponential, the domain and range may extend beyond the given table.

Remember:

• Interval notation uses parentheses for open intervals (values not included) and brackets for closed intervals (values included).
• Infinity (∞) and negative infinity (-∞) are always used with parentheses.

This answer key provides a framework for solving domain and range problems. Remember to replace these examples with the actual problems from your worksheet. If you have specific questions from your worksheet, feel free to provide them for a more tailored answer key.