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Precalculus: Transformations of Functions

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이 집합의 용어 (20)

  • What is a vertical shift upward of a function?
    The graph of \(y=f(x)+c\) is the graph of \(y=f(x)\) shifted up c units.
  • What is a vertical shift downward of a function?
    The graph of \(y=f(x)-c\) is the graph of \(y=f(x)\) shifted down c units.
  • How does the graph of \(y=f(x+c)\) transform?
    It is the graph of \(y=f(x)\) shifted left by c units.
  • How does the graph of \(y=f(x-c)\) transform?
    It is the graph of \(y=f(x)\) shifted right by c units.
  • What is the reflection of a function about the x-axis?
    The graph of \(y=-f(x)\) is the graph of \(y=f(x)\) reflected about the x-axis.
  • What happens when a function is vertically stretched?
    The graph of \(y=cf(x)\) is vertically stretched if c > 1, making the graph taller.
  • What happens when a function is vertically shrunk?
    The graph of \(y=cf(x)\) is vertically shrunk if 0 < c < 1, making the graph shorter.
  • How do you translate the point (x, y) for a vertical shift up by c units?
    The point (x, y) moves to (x, y + c).
  • How do you translate the point (x, y) for a vertical shift down by c units?
    The point (x, y) moves to (x, y - c).
  • How do you translate the point (x, y) for a horizontal shift left by c units?
    The point (x, y) moves to (x - c, y).
  • How do you translate the point (x, y) for a horizontal shift right by c units?
    The point (x, y) moves to (x + c, y).
  • How do you reflect a point (x, y) about the x-axis?
    The point (x, y) moves to (x, -y).
  • How do you vertically stretch a point (x, y) by a factor of c?
    The point (x, y) moves to (x, cy).
  • How do you vertically shrink a point (x, y) by a factor of c?
    The point (x, y) moves to (x, cy) where 0 < c < 1.
  • What is the parent function for quadratic functions?
    The parent function is \(f(x)=x^2\).
  • What is the parent function for the absolute value function?
    The parent function is \(f(x)=|x|\).
  • How does the function \(g(x)=(x+5)^2\) transform the parent function \(x^2\)?
    It shifts the graph left 5 units.
  • How does the function \(h(x)=-(x+2)^2\) transform the parent function \(x^2\)?
    It shifts the graph left 2 units and reflects it about the x-axis.
  • What is the effect of the function \(f(x)=x^2-2\) on the parent function \(x^2\)?
    It shifts the graph down 2 units.
  • What is the effect of the function \(h(x)=(x-2)^2\) on the parent function \(x^2\)?
    It shifts the graph right 2 units.