Graph y=cos(x)+2

Problem

y=cos(x)+2

Solution

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

2. Determine the vertical shift by looking at the constant term. The +2 indicates a vertical shift upward by 2 units.

3. Calculate the new range and midline. The midline moves from y=0 to y=2 The maximum value becomes 1 + 2 = 3a*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 + 2 = 1$.

4. Plot key points over one period [0,2*π]

• At x=0 y=cos(0)+2=1+2=3

• At x=π/2 y=cos(π/2)+2=0+2=2

• At x=π y=cos(π)+2=−1+2=1

• At x=(3*π)/2 y=cos((3*π)/2)+2=0+2=2

• At x=2*π y=cos(2*π)+2=1+2=3

5. Sketch the curve by connecting these points with a smooth, periodic wave shape.

Final Answer

y=cos(x)+2

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