Graphs of radical functions Flashcard

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•
Mathematics
•
9th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is a radical function?
Back
A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is f(x) = √(g(x)), where g(x) is a polynomial.
2.
FLASHCARD QUESTION
Front
What is the domain of a radical function?
Back
The domain of a radical function is the set of all x-values for which the expression under the radical is non-negative. For example, for f(x) = √(x - 4), the domain is x ≥ 4.
3.
FLASHCARD QUESTION
Front
How does the graph of f(x) = √(x) differ from f(x) = -√(x)?
Back
The graph of f(x) = √(x) opens upwards, while f(x) = -√(x) opens downwards, reflecting the graph across the x-axis.
4.
FLASHCARD QUESTION
Front
What effect does adding a constant outside the radical have on the graph?
Back
Adding a constant outside the radical shifts the graph vertically. For example, f(x) = √(x) + 2 shifts the graph up by 2 units.
5.
FLASHCARD QUESTION
Front
What effect does adding a constant inside the radical have on the graph?
Back
Adding a constant inside the radical shifts the graph horizontally. For example, f(x) = √(x - 3) shifts the graph right by 3 units.
6.
FLASHCARD QUESTION
Front
What is the range of the function f(x) = √(x - 4)?
Back
The range of f(x) = √(x - 4) is [0, ∞) because the square root function outputs non-negative values.
7.
FLASHCARD QUESTION
Front
How do you determine the x-intercept of a radical function?
Back
To find the x-intercept, set the function equal to zero and solve for x. For example, for f(x) = √(x - 4), set √(x - 4) = 0, which gives x = 4.
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