Graph y=cos(x)-1

Problem

y=cos(x)−1

Solution

1. Identify the parent function, which is y=cos(x) This function has a period of 2*π an amplitude of 1 and oscillates between 1 and −1

2. Determine the vertical shift by looking at the constant term −1 This indicates that the entire graph of y=cos(x) is shifted downward by 1 unit.

3. Calculate the new range by subtracting 1 from the original maximum and minimum values. The maximum value becomes 1 - 1 = 0a*n*d(t)*h*e*m*i*n*i*m*u*m*v*a*l*u*e*b*e*c*o*m*e*s()1 - 1 = -2$.

4. Identify key points for one period [0,2*π] The point (0,1) moves to (0,0) (π/2,0) moves to (π/2,−1) (π,−1) moves to (π,−2) ((3*π)/2,0) moves to ((3*π)/2,−1) and (2*π,1) moves to (2*π,0)

5. Sketch the curve by plotting these key points and drawing a smooth wave that repeats every 2*π units along the xaxis.

Final Answer

y=cos(x)−1

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