Functions Flashcards

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Questions and Answers

What is the definition of a Constant Function?

  • f(x)=x
  • f(x)=√x
  • f(x)=c (correct)
  • f(x)=m(x)+b

What is the range (R) of a Constant Function?

[c,c] or {c}

A Constant Function is classified as even.

True (A)

What is the definition of an Identity Function?

<p>f(x)=x (C)</p>
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What is the domain (D) of an Identity Function?

<p>(-∞,∞)</p>
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An Identity Function is classified as odd.

<p>True (A)</p>
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What is the general formula of a Linear Function?

<p>f(x)=m(x)+b (D)</p>
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What is the classification of a Linear Function?

<p>Neither, unless y=x</p>
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What is the definition of an Absolute Value Function?

<p>f(x)=lxl (C)</p>
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What is the range (R) of an Absolute Value Function?

<p>[0,∞)</p>
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An Absolute Value Function is classified as even.

<p>True (A)</p>
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What is the formula for a Squared Function?

<p>f(x)=x^2 (A)</p>
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What is the classification of a Squared Function?

<p>Even</p>
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What is the definition of a Cube Function?

<p>f(x)=x^3 (A)</p>
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What is the classification of a Cube Function?

<p>Odd</p>
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What is the formula for a Square Root Function?

<p>f(x)=√x (B)</p>
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What is the domain (D) of a Square Root Function?

<p>[0,∞)</p>
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A Square Root Function is classified as even.

<p>False (B)</p>
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What is the definition of a Cube Root Function?

<p>f(x)=3√x (B)</p>
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What is the classification of a Cube Root Function?

<p>Odd</p>
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What is the formula for a Reciprocal Function?

<p>f(x)=1/x (D)</p>
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What is the domain (D) of a Reciprocal Function?

<p>(-∞,0)U(0,∞)</p>
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A Reciprocal Function is classified as odd.

<p>True (A)</p>
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What is the formula for Reciprocal Squared?

<p>1/x^2 (C)</p>
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What is the classification of Reciprocal Squared?

<p>Symmetric about the y-axis</p>
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Flashcards

Constant Function

A function where the output is always the same constant value, no matter what the input is.

Identity Function

A function where the output is always equal to the input.

Linear Function

A function whose graph is a straight line. It can be represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Absolute Value Function

A function that represents the distance of a number from zero, always resulting in a non-negative value.

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Squared Function

A function where the input is squared, resulting in a parabolic graph.

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Cube Function

A function where the input is cubed, resulting in a graph with both positive and negative values.

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Square Root Function

A function that finds the principal square root of the input. The input must be non-negative.

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Cube Root Function

A function that finds the cube root of the input. It can take any real number as input.

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Reciprocal Function

A function where the output is the inverse of the input. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

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Reciprocal Squared

A function where the output is the square of the reciprocal of the input. It has no x-intercept or y-intercept and is symmetrical about the y-axis.

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Domain

The set of all possible input values for a function.

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Range

The set of all possible output values for a function.

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Even Function

A function where f(-x) = f(x) for all x in the domain.

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Odd Function

A function where f(-x) = -f(x) for all x in the domain.

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Y-Intercept

The point where the graph of a function intersects the y-axis.

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Slope

The rate of change of a linear function, represented by the letter 'm' in the equation f(x) = mx + b.

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Asymptote

A line that the graph of a function approaches as x approaches positive or negative infinity. In other words, the function gets arbitrarily close to this line but never reaches it.

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Vertical Asymptote

A vertical line that a function approaches as x approaches a specific value. The function gets infinitely close to this line but never reaches it.

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Horizontal Asymptote

A horizontal line that a function approaches as x approaches positive or negative infinity. The function gets infinitely close to this line but never reaches it.

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Turning Point

A point on the graph of a function where the slope is zero. This indicates a change in the direction of the graph.

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Continuous Function

A function that can be represented by a single equation for all real numbers.

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Discontinuous Function

A function that has breaks or jumps in its graph.

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One-to-One Function

A function that results in a unique output for each unique input.

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Many-to-One Function

A function that may have multiple inputs that lead to the same output.

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Rational Function

A function that can be expressed as a ratio of two polynomials.

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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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