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Questions and Answers
Identify the domain of the function { (6,-3), (2,9), (-1,-3) }. Write the letter of the correct choice in the blank.
Identify the domain of the function { (6,-3), (2,9), (-1,-3) }. Write the letter of the correct choice in the blank.
- D: {-1,2,6} (correct)
- D: {-3,-1,2,6,9}
- D: {-3,9}
- None of these
Identify the domain of the function defined by the mappings -3→7, 0 ↑, 9→17.
Identify the domain of the function defined by the mappings -3→7, 0 ↑, 9→17.
- D: {-3,0,9} (correct)
- None of these
- D: {-3,0,7,9,17}
- D: {7,17}
Identify the domain of the function f(x) = √(x+1).
Identify the domain of the function f(x) = √(x+1).
- D: {x | x ≠-1} (correct)
- None of these
- D: {x | x ≠0}
- D: R
Identify the domain of the function g(x) = x + √3.
Identify the domain of the function g(x) = x + √3.
Identify the domain of the function h(x) = (x - 1) / (x² + 5x + 6).
Identify the domain of the function h(x) = (x - 1) / (x² + 5x + 6).
Identify the domain of the function f(x) = (√(x-5)) / x.
Identify the domain of the function f(x) = (√(x-5)) / x.
Match each function with its parent function type.
Match each function with its parent function type.
Flashcards
What is a Domain?
What is a Domain?
The set of all first elements (x-values) in a relation or function.
Domain from Ordered Pairs
Domain from Ordered Pairs
For a set of ordered pairs, it's the set of all first elements.
Domain from Mappings
Domain from Mappings
For mappings, it's the set of input values that are being mapped.
Domain of f(x) = √(x+1)
Domain of f(x) = √(x+1)
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Domain of g(x) = x + √3
Domain of g(x) = x + √3
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Domain of h(x) = (x - 1) / (x² + 5x + 6)
Domain of h(x) = (x - 1) / (x² + 5x + 6)
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Domain of f(x) = (√(x-5)) / x
Domain of f(x) = (√(x-5)) / x
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Study Notes
Domain Identification for Functions
- Domain refers to the set of all possible input values (x-values) for a function.
- For the function with points (6,-3), (2,9), (-1,-3), the domain is {6, 2, -1}.
- The options for the domains of various functions:
- For { (6,-3), (2,9), (-1,-3) }, correct domain is D: {-1,2,6}.
- For the input-output relationship -3→7, 0↑, 9→17, correct domain is D: {-3,0,9}.
- For f(x) = √(x+1), domain is D: {x|x≥-1}.
- For g(x) = x + √3, the domain is all real numbers (R).
- For h(x) = (x-1)/(x²+5x+6), domain excludes points where the denominator is zero (x≠-2, x≠-3).
Function Types and Their Parent Functions
- Identifying parent functions helps categorize different functions:
- f(x) = 3 corresponds to a constant function (B).
- f(x) = (1/4)x - 2 is a linear function (E).
- f(x) = x³ + x² is categorized as a cubic function (D).
- Various graphs represent reciprocal functions and square root functions, denoted as G and H, respectively.
Restricted Domains due to Square Roots
- Functions involving square roots have restrictions:
- For f(x) = √(x-5)/x, x must be greater than or equal to 5 (x≥5) to keep the expression defined.
- At the same time, x cannot equal 0 since it would create division by zero.
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