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.
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Domain, Range, and End Behavior of Functions
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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.