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Transformations quiz #1 Flashcards

Transformations quiz #1
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  • What is the effect on the graph of f(x) = |3x - 4| when it is replaced by f(x) + 3?
    Replacing f(x) with f(x) + 3 results in a vertical shift of the graph upward by 3 units.
  • What is the equation of the translated function, g(x), if f(x) = x^2 and the graph is shifted horizontally by h units and vertically by k units?
    The equation of the translated function is g(x) = (x - h)^2 + k, where h is the horizontal shift and k is the vertical shift.
  • What happens to the y-values of a function when it is reflected over the x-axis?
    The y-values change sign, becoming their opposites. This is represented by multiplying the function by -1.
  • How does multiplying a function by a constant greater than 1 outside the function affect its graph?
    It causes a vertical stretch, making the graph taller by that factor. All y-values are multiplied by the constant.
  • What transformation occurs when a constant between 0 and 1 is multiplied inside the function's argument?
    This results in a horizontal stretch of the graph. The graph becomes wider as x-values are scaled by the reciprocal of the constant.
  • If a function is shifted horizontally by h units to the right, how is this represented in function notation?
    It is written as f(x - h). The minus sign indicates a shift to the right by h units.
  • What is the effect on the domain and range of a function when it is shifted vertically?
    A vertical shift changes the range by adding or subtracting the shift value to all y-values. The domain remains unchanged.
  • How do you determine the new equation after reflecting f(x) = x + 2 over the x-axis?
    You multiply the entire function by -1, resulting in -x - 2. This flips the graph over the x-axis.
  • What does a horizontal compression by a factor of c > 1 look like in function notation?
    It is represented as f(cx), where c > 1. The graph becomes narrower as x-values are divided by c.
  • When combining a reflection and a horizontal shift, how is the transformed function written?
    The function is written as -f(x + h) for a reflection over the x-axis and a shift h units to the left. The negative sign reflects, and the plus h shifts left.