Questions and Answers
What is the definition of a Constant Function?
What is the range (R) of a Constant Function?
[c,c] or {c}
A Constant Function is classified as even.
True
What is the definition of an Identity Function?
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What is the domain (D) of an Identity Function?
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An Identity Function is classified as odd.
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What is the general formula of a Linear Function?
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What is the classification of a Linear Function?
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What is the definition of an Absolute Value Function?
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What is the range (R) of an Absolute Value Function?
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An Absolute Value Function is classified as even.
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What is the formula for a Squared Function?
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What is the classification of a Squared Function?
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What is the definition of a Cube Function?
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What is the classification of a Cube Function?
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What is the formula for a Square Root Function?
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What is the domain (D) of a Square Root Function?
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A Square Root Function is classified as even.
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What is the definition of a Cube Root Function?
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What is the classification of a Cube Root Function?
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What is the formula for a Reciprocal Function?
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What is the domain (D) of a Reciprocal Function?
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A Reciprocal Function is classified as odd.
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What is the formula for Reciprocal Squared?
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What is the classification of Reciprocal Squared?
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Study Notes
Constant Function
- Defined as f(x)=c, where c is a constant value.
- Domain: D=(-∞,∞)
- Range: R=[c,c] or {c}, meaning it takes a single value.
- Characterized as an even function.
Identity Function
- Expressed as f(x)=x, representing a direct correlation.
- Domain: D=(-∞,∞)
- Range: R=(-∞,∞), implying all real numbers are possible outputs.
- Classified as an odd function.
Linear Function
- Given by the formula f(x)=m(x)+b, where m≠0.
- Domain: D=(-∞, ∞)
- Range: R=(-∞,∞), encompassing all real numbers.
- Neither even nor odd, unless specified as y=x.
Absolute Value Function
- Formulated as f(x)=|x|, which reflects value to be non-negative.
- Domain: D=(-∞,∞)
- Range: R=[0,∞), indicating outputs are zero or positive.
- Recognized as an even function.
Squared Function
- Represented as f(x)=x^2, emphasizing squaring of input values.
- Domain: D=(-∞,∞)
- Range: R=[0,∞), confirming all outputs are non-negative.
- Classified as an even function.
Cube Function
- Defined by f(x)=x^3, which illustrates cubic relationships.
- Domain: D=(-∞,∞)
- Range: R=(-∞,∞), indicating all real numbers can be outputs.
- Identified as an odd function.
Square Root Function
- Expressed by f(x)=√x, showcasing principal square root extraction.
- Domain: D=[0,∞), restricted to non-negative inputs.
- Range: R=[0,∞), confirming non-negative outputs.
- Classified as neither even nor odd.
Cube Root Function
- Formulated as f(x)=³√x, representing the cube root.
- Domain: D=(-∞,∞)
- Range: R=(-∞,∞), covering all real numbers.
- Identified as an odd function.
Reciprocal Function
- Given by f(x)=1/x, signifying the inverse relationship.
- Domain: D=(-∞,0)U(0,∞) to exclude zero.
- Range: R=(-∞,0)U(0,∞), ensuring outputs do not include zero.
- Recognized as an odd function.
Reciprocal Squared
- Represented as f(x)=1/x², involving the square of the reciprocal.
- Has no x-intercept and no y-intercept.
- Vertical asymptote at x=0 and horizontal asymptote at y=0.
- Symmetric about the y-axis.
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Description
Test your knowledge on various types of functions with this engaging set of flashcards. Covering Constant, Identity, Linear, Absolute Value, and Quadratic Functions, you'll explore their definitions, domains, and ranges. Perfect for reinforcing your understanding of mathematics!
