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Questions and Answers
What is the domain of the squaring function $f(x) = x^2$?
What is the domain of the squaring function $f(x) = x^2$?
- All real numbers (correct)
- Numbers between $0$ and $1$
- All positive real numbers
- All nonnegative numbers
What is the range of the squaring function $f(x) = x^2$?
What is the range of the squaring function $f(x) = x^2$?
- All real numbers
- Negative numbers only
- All nonnegative numbers (correct)
- All positive real numbers
What is the range of the function $g(x) = rac{1}{ ext{sqrt}{2x+9}}$ for $x ext{ in } [0, 8]$?
What is the range of the function $g(x) = rac{1}{ ext{sqrt}{2x+9}}$ for $x ext{ in } [0, 8]$?
- [5, ext{undefined}]
- [0, 5]
- [0, 3]
- [3, 5] (correct)
For the function $g(x) = ext{sqrt}{2x+9}$, what is the value of $g(0)$?
For the function $g(x) = ext{sqrt}{2x+9}$, what is the value of $g(0)$?
The domain of the function $g(x) = ext{sqrt}{2x+9}$ is restricted to which interval?
The domain of the function $g(x) = ext{sqrt}{2x+9}$ is restricted to which interval?
Flashcards
Domain of a function
Domain of a function
The set of all possible input values (x-values) for which a function is defined.
Range of a function
Range of a function
The set of all possible output values (y-values) that a function can produce.
Squaring Function Domain
Squaring Function Domain
All real numbers; ( (-\infty, \infty) )
Squaring Function Range
Squaring Function Range
All non-negative real numbers; ([0, \infty)).
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Domain of a function with square root
Domain of a function with square root
Input values such that the term inside the square root is greater than or equal to zero.
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Example 2: The Squaring Function
- The problem is to find the domain and range of the squaring function
- The function is f(x) = x2, where x is a real number
- The domain of f is explicitly given as the set of all real numbers.
- As x runs through all the real numbers, x2 runs through all the nonnegative numbers
- The range is therefore [0, ∞)
Example 3:
- The problem is to find the domain and range of the function g(x) = √(2x + 9), x ∈ [0, 8]
- The domain of g is given as the closed interval [0, 8].
- g(0) = √(2(0) + 9) = √9= 3
- g(8) = √(2(8) + 9) = √25 = 5
- The range is therefore [3, 5]
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