Podcast
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
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Domain of a function with square root
Domain of a function with square root
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Study Notes
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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Description
This quiz focuses on determining the domain and range of specific mathematical functions, including the squaring function and the square root function. Participants will explore how these functions behave over given intervals and how to express their domains and ranges correctly.
