Graph f(x)=sin(x)-5

Problem

ƒ(x)=sin(x)−5

Solution

1. Identify the parent function, which is y=sin(x) This function has a period of 2*π an amplitude of 1 and oscillates around the midline y=0

2. Determine the vertical shift by looking at the constant term −5 This indicates that the entire graph of sin(x) is shifted downward by 5 units.

3. Identify the new midline, which is the horizontal line y=−5 The graph will oscillate between a maximum value and a minimum value relative to this line.

4. Calculate the range by applying the amplitude of 1 to the new midline. The maximum value is −5+1=−4 and the minimum value is −5−1=−6

5. Plot key points over one period [0,2*π] The points (0,−5) (π/2,−4) (π,−5) ((3*π)/2,−6) and (2*π,−5) define the shape of the wave.

6. Draw the smooth curve passing through these points and extend it in both directions to complete the graph.

Final Answer

ƒ(x)=sin(x)−5

Want more problems? Check here!