Domain, Range, and End Behavior of Functions
Explore and analyze the domain, range, and end behavior of various functions at a Grade 12 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 complete answers. For graphing questions, use the provided coordinate plane. Show all your work.
1. Determine the domain and range of the function f(x) = √(x - 3) + 2.
2. Determine the domain and range of the function g(x) = (x + 1) / (x^2 - 4).
3. Which of the following best describes the end behavior of the function h(x) = -2x^3 + 5x - 1?
As x → ∞, h(x) → ∞; as x → -∞, h(x) → -∞
As x → ∞, h(x) → -∞; as x → -∞, h(x) → ∞
As x → ∞, h(x) → ∞; as x → -∞, h(x) → ∞
As x → ∞, h(x) → -∞; as x → -∞, h(x) → -∞
4. What is the end behavior of the function k(x) = 4x^4 - 3x^2 + 7?
As x → ∞, k(x) → ∞; as x → -∞, k(x) → ∞
As x → ∞, k(x) → -∞; as x → -∞, k(x) → -∞
As x → ∞, k(x) → ∞; as x → -∞, k(x) → -∞
As x → ∞, k(x) → -∞; as x → -∞, k(x) → ∞
5. The domain of a polynomial function is always .
6. For a rational function, vertical asymptotes occur where the is equal to zero and the numerator is non-zero.
7. The range of the function f(x) = x^2 is all real numbers.
True
False
8. If the degree of the numerator is greater than the degree of the denominator in a rational function, there is a horizontal asymptote at y=0.
True
False
9. Graph the function f(x) = (x - 2)^2 - 1. Then, state its domain, range, and end behavior.
Domain:
Range:
End Behavior: