Sketch a graph of a sine function with a horizontal and vertical translation. Your sine function must have an amplitude other than 1 and cross through
the x-axis in two locations.
State the equation of the sine function you sketched. Identify the translations used.
Determine the equations ( Vertex and standard form ) of the parabolas that are identical to the sine function You drew.
The domain and range of each parabola, include the vertex of each parabola and the zeros of the parabola if they exist.
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You need to remember the rules that tell when the graph of function f(x) translated horizonatlly by c units or vertically by b units such that:
- f(x-c) denotes the modified function whose graph is the graph of f(x) translated horizontally by c units to the right if c>0 or to the left if c<0.
- f(x)+b denotes the modified function whose graph is the graph of f(x) translated vertically by b units up if b>0 down if b<0.
Consider the function `g(x) = sin (x-pi/2) + 2` . The function g(x) denotes the modified function f(x) and you may get the graph of g(x) translating the graph of f(x) horizontally, to the left, by pi/2 and vertically, up, by 2.
Hence, the black curve denotes the graph of `f(x)=sin x` and the red curve denotes the graph of modified function `g(x) = sin (x-pi/2) + 2.`
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