Mathematics
Grade 11
15 min
Domain and range of radical functions
Domain and range of radical functions
What you'll learn
- Identify whether a multiplication or division sentence (up to 12 x 12) is true or false with 80% accuracy.
- Solve multiplication and division problems (up to 12 x 12) to determine if a given number sentence is true or false.
- Explain why a multiplication or division sentence (up to 12 x 12) is true or false using mathematical reasoning.
- Apply knowledge of multiplication and division facts (up to 12 x 12) to correctly evaluate at least 4 out of 5 true/false statements.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define domain and range in the context of radical functions.
Determine the domain of a radical function with an even index by setting the radicand greater than or equal to zero.
Determine the domain of a radical function with an odd index.
Determine the range of a radical function by analyzing its vertical shift and leading coefficient.
Write the domain and range of radical functions using correct interval notation.
Analyze how transformations (shifts, reflections) affect the domain and range of a parent radical function.
Ever wondered how engineers calculate the maximum load a curved support can handle or how a GPS calculates the shortest distance between two points? 🗺️ The answers lie in understanding the limits of functions, just like the ones we'...
2
Key Concepts & Vocabulary
TermDefinitionExample
Radical FunctionA function that contains a variable within the radicand. The general form is f(x) = a * \sqrt[n]{g(x)} + k.f(x) = 2\sqrt{x-3} + 5
RadicandThe expression found inside the radical symbol (√).In f(x) = \sqrt{x-3}, the radicand is 'x-3'.
IndexThe small number outside the radical symbol that indicates the type of root. If no index is written, it is assumed to be 2 (a square root).In f(x) = \sqrt[3]{x}, the index is 3 (a cube root).
DomainThe set of all possible input values (x-values) for which the function is defined.For f(x) = \sqrt{x}, the domain is [0, \infty) because we cannot take the square root of a negative number in the real number system.
RangeThe set of all possible output values (y-values) that the function can produce.For f(x) = \sq...
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Core Formulas
Domain of Even-Indexed Roots
For f(x) = a\sqrt[n]{g(x)} + k, where n is even, the domain is found by solving the inequality: g(x) \geq 0
Use this rule for square roots, fourth roots, etc. The expression inside the radical (the radicand) cannot be negative, as this would result in a non-real number.
Domain of Odd-Indexed Roots
For f(x) = a\sqrt[n]{g(x)} + k, where n is odd, the domain is all real numbers.
Use this rule for cube roots, fifth roots, etc. You can take an odd root of any real number, positive or negative, so there are no restrictions on the input.
Range of Even-Indexed Roots
For f(x) = a\sqrt[n]{g(x)} + k, where n is even: If a > 0, the range is [k, \infty). If a < 0, the range is (-\infty, k].
The range is determined by the vertical shift (k) and t...
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Challenging
What is the domain of the function f(x) = √(x² - 9)?
A.[-3, 3]
B.[3, ∞)
C.(-∞, -3] ∪ [3, ∞)
D.(-∞, ∞)
Challenging
The function f(x) = √x is reflected across the x-axis, reflected across the y-axis, and then shifted 4 units to the right. What is the domain of the resulting function?
A.[4, ∞)
B.(-∞, -4]
C.[-4, ∞)
D.(-∞, 4]
Challenging
For the function f(x) = a√(x + 2) - 6, the range is [-6, ∞). What must be true about the parameter 'a'?
A.a < 0
B.a > 0
C.a = 0
D.a can be any real number
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Frequently asked questions
What grade level is "Domain and range of radical functions"?
Domain and range of radical functions is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Domain and range of radical functions?
You'll be able to: Identify whether a multiplication or division sentence (up to 12 x 12) is true or false with 80% accuracy; Solve multiplication and division problems (up to 12 x 12) to determine if a given number sentence is true or false….
Is "Domain and range of radical functions" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Domain and range of radical functions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.