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Common Functions quiz

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  • What is the domain and range of the constant function f(x) = c?
    The domain is all real numbers, and the range is the single value c.
  • What does the identity function f(x) = x output for any input x?
    It outputs the same value as the input, so f(x) = x for all x.
  • What is the domain and range of the square function f(x) = x^2?
    The domain is all real numbers, and the range is [0, ∞).
  • What shape does the graph of the square function f(x) = x^2 form?
    It forms a parabola opening upwards.
  • What is the domain and range of the cube function f(x) = x^3?
    Both the domain and range are all real numbers.
  • What is the domain and range of the square root function f(x) = √x?
    The domain and range are [0, ∞).
  • What is the domain and range of the cube root function f(x) = ∛x?
    Both the domain and range are all real numbers.
  • What is the slope-intercept form of a line and what do m and b represent?
    The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
  • How do you find the y-intercept of a line from its graph?
    The y-intercept is the y-value where the graph crosses the y-axis, at x = 0.
  • What is the standard form of a quadratic function and what is its graph called?
    The standard form is f(x) = ax^2 + bx + c, and its graph is a parabola.
  • What is the axis of symmetry for a parabola and how is it related to the vertex?
    The axis of symmetry is a vertical line passing through the vertex, dividing the parabola in half.
  • What are the requirements for a function to be a polynomial function?
    All exponents must be positive whole numbers, and the graph must be smooth and continuous.
  • What is a rational function and how do you find its domain restrictions?
    A rational function is a fraction of polynomials, and its domain excludes values that make the denominator zero.
  • What are the requirements for the base of an exponential function?
    The base must be constant, positive, and not equal to 1.
  • How are logarithmic functions related to exponential functions, and how is their graph obtained?
    Logarithmic functions are the inverse of exponential functions, and their graph is a reflection of the exponential graph over the line y = x.