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College Algebra: Functions, Graphs, and Applications

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이 집합의 용어 (20)

  • What is the formula for the height of a falling rock from 20 meters after x seconds?
    The height H(x) is given by \(H(x)=20-4.9x^2\).
  • How do you find the height of the rock at a specific time using the height function?
    Substitute the time value into \(H(x)=20-4.9x^2\) and calculate.
  • How do you determine when the rock hits the ground using the height function?
    Set \(H(x)=0\) and solve for x.
  • What is the domain of a function given by a graph?
    The set of all x-values for which the function is defined.
  • What is the range of a function given by a graph?
    The set of all y-values that the function attains.
  • How do you find the x-intercepts of a function from its graph?
    Identify points where the graph crosses the x-axis (y=0).
  • How do you find the y-intercept of a function from its graph?
    Identify the point where the graph crosses the y-axis (x=0).
  • What does it mean for a function to be increasing on an interval?
    The function's values rise as x increases over that interval.
  • What does it mean for a function to be decreasing on an interval?
    The function's values fall as x increases over that interval.
  • How do you determine if a function is even, odd, or neither from its graph?
    Even functions are symmetric about the y-axis; odd functions have rotational symmetry about the origin.
  • How do you find the zeros of a function from its graph?
    The zeros are the x-values where the function crosses or touches the x-axis.
  • What is a piecewise function?
    A function defined by different expressions over different intervals of the domain.
  • How do you evaluate a piecewise function at a given x-value?
    Determine which piece applies to the x-value and use that expression to find the output.
  • What is the parent function of a quadratic function?
    The parent function is \(f(x)=x^2\).
  • How do you describe transformations from a parent function to a given function?
    List shifts, stretches/compressions, and reflections in the correct order.
  • How do you compute the monthly cost for a tablet plan with a piecewise cost function?
    Use the appropriate formula based on the number of gigabytes used.
  • What is the formula for demand D related to price p if demand is inversely related to price?
    Demand D is proportional to \(\frac{1}{p}\).
  • How do you express demand for candy in terms of price if price is \$2.75 and 156 bags are sold?
    Use the inverse relationship to find the constant and write \(D=\frac{k}{p}\).
  • How do you find the number of bags sold if the price changes to \$3?
    Substitute the new price into the demand function and solve for D.
  • What is the effect of gravity on the height of a falling object over time?
    Height decreases quadratically with time due to gravity, modeled by \(H(x)=20-4.9x^2\).