Domain, Range, and End Behavior of Functions
This worksheet focuses on understanding and determining the domain, range, and end behavior of various functions at a Grade 11 level, including polynomial, rational, and radical functions.
Includes
Standards
Domain, Range, and End Behavior of Functions
Name:
Date:
Score:
Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. For the function graphed below, identify its domain and range.
Domain:
Range:
2. Determine the domain of the function f(x) = √(x - 3). The domain is .
3. What is the range of the function f(x) = x² + 2? The range is .
4. Find the domain of the rational function f(x) = 1 / (x - 5). The domain is .
5. Describe the end behavior of the function f(x) = -2x³ + 4x² - x + 1.
As x → ∞, f(x) →
As x → -∞, f(x) →
6. Describe the end behavior of the function g(x) = 3x⁴ - 2x² + 5.
As x → ∞, g(x) →
As x → -∞, g(x) →
7. Which of the following functions has end behavior where f(x) → ∞ as x → ∞ and f(x) → -∞ as x → -∞?
f(x) = x²
f(x) = -x³
f(x) = x³
f(x) = -x²
8. Consider the function h(x) = √(x + 4) - 1.
a) Determine the domain of h(x).
b) Determine the range of h(x).
c) Describe the end behavior of h(x) as x approaches the limits of its domain.
Related Worksheets
Exponential Function Manipulation Worksheet
A Grade 11 math worksheet focusing on manipulating and understanding exponential functions, including their graphs, properties, and transformations.
Transformation of Graphs Worksheet
Grade 11 Math worksheet focusing on transformations of functions, including translations, reflections, stretches, and compressions.
Function Transformation Worksheet - Grade 11
Explore function transformations including translations, reflections, stretches, and compressions with this comprehensive worksheet for Grade 11 Math students.
Function Composition Exploration
This worksheet focuses on understanding and applying function composition with various types of functions, suitable for Grade 11 mathematics students.
Parent Functions and Transformations Worksheet
Explore parent functions and their transformations including translations, reflections, stretches, and compressions with this Grade 11 math worksheet.
Domain and Range Worksheet
Grade 11 Math worksheet focusing on identifying the domain and range of various functions from graphs, equations, and real-world scenarios.
Function Graphs Worksheet
Explore and analyze various function graphs including linear, quadratic, exponential, and logarithmic functions. Practice identifying key features and transformations.
Functions and Mapping Worksheet
Grade 11 Math worksheet focusing on understanding and applying concepts of functions, relations, domain, range, and various types of mapping.