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Questions and Answers
What is the domain of the function $y = 3 , \sqrt{x}$?
What is the domain of the function $y = 3 , \sqrt{x}$?
x \geq 0
How does the graph of $y = \sqrt{x} + 2$ compare to the graph of the parent square root function?
How does the graph of $y = \sqrt{x} + 2$ compare to the graph of the parent square root function?
- The graph is a vertical shift of the parent function 2 units down.
- The graph is a horizontal shift of the parent function 2 units right.
- The graph is a vertical shift of the parent function 2 units up. (correct)
- The graph is a horizontal shift of the parent function 2 units left.
Which graph represents $y = 3 , \sqrt{x}$?
Which graph represents $y = 3 , \sqrt{x}$?
- Graph D (correct)
- Graph B
- Graph C
- Graph A
The range of which function includes -4?
The range of which function includes -4?
Which of the following describes the graph of $y = \sqrt{-4x - 36}$ compared to the parent square root function?
Which of the following describes the graph of $y = \sqrt{-4x - 36}$ compared to the parent square root function?
Which function has the same domain as $y = 2 , \sqrt{x}$?
Which function has the same domain as $y = 2 , \sqrt{x}$?
What is the domain of the function $y = 3 , \sqrt{x - 1}$?
What is the domain of the function $y = 3 , \sqrt{x - 1}$?
Which of the following is the graph of $y = -4 , \sqrt{x}$?
Which of the following is the graph of $y = -4 , \sqrt{x}$?
Which graph represents $y = 3 , \sqrt{x - 5}$?
Which graph represents $y = 3 , \sqrt{x - 5}$?
Which statement best describes $f(x) = -2 , \sqrt{x} - 7 + 1$?
Which statement best describes $f(x) = -2 , \sqrt{x} - 7 + 1$?
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Study Notes
Domain and Range of Radical Functions
- The function ( y = 3\sqrt{x} ) has a domain of ( x \geq 0 ).
- A general property of radical functions: the domain typically consists of all ( x ) values for which the expression under the square root is non-negative.
- The range of functions like ( y = 3\sqrt{x} ) is ( y \geq 0 ).
Transformations of Radical Functions
- The function ( y = \sqrt{x} + 2 ) represents a vertical shift of the parent square root function, moving it 2 units upwards.
- A function of the form ( y = -\sqrt{-4x - 36} ) reflects over the x-axis and is stretched by a factor of 2, translating 9 units horizontally.
- For the function ( y = 3\sqrt{x} - 5 ), the graph shifts downward by 5 units compared to the parent function.
Identifying Function Graphs
- Recognizing different forms of radical functions, such as ( y = -4\sqrt{x} ), is crucial to understanding their graphical representations.
- The transformation characteristics provide insight into how the graph is altered from the parent function based on changes in coefficients and added constants.
Specific Values in Functions
- The statement regarding ( f(x) = -2\sqrt{x} - 7 + 1 ) indicates that -6 is not present in the domain of ( f(x) ), implying the domain excludes non-negative square roots.
- Understanding whether a specific value is in the domain or range helps to master graph interpretations.
Function Comparisons
- Identification of functions that share the same domain as another, e.g., ( y = 2\sqrt{x} ), reinforces the concept of domain similarity in radical expressions.
- The importance of horizontal and vertical shifts must not be overlooked when making comparisons between graphs.
Visual Representation
- Graphical understanding is vital when identifying transformations; visual comparisons enhance comprehension of shifts, stretches, and reflections in radical functions.
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