How do you graph #y=1/2cosx+3#?

Question

Josiah Anderson · Accepted Answer

your graph is moved up vertically 3 units and its amplitude is cut in half as compared to the parent function #y=cosx#

Use this standard formula to convert from the parent function #y=cosx#

#y=acos(bx-c)+d#

a = amplitude b = horizontal stretch c = horizontal shift d = vertical shift

your function has a amplitude of #1/2# and a vertical shift of #+3#

#y=cosx# has a amplitude of 1 and no shift:

graph{cosx [-10, 10, -5, 5]}

#y=1/2cosx + 3#

So your graph is moved up vertically 3 units and its amplitude is cut in half:

graph{1/2cosx + 3 [-10, 10, -5, 5]}

Grace Ashcraft · Answer

undefined To graph the function y = (1/2)cos(x) + 3, you can follow these steps:

1. Identify the key components of the function: The coefficient of cos(x) is 1/2, which indicates a vertical stretch/compression, and the constant term is 3, which indicates a vertical shift.

2. Plot key points: Start by plotting the key points of the cosine function, which include the maximum, minimum, and intercepts. The maximum value of cos(x) is 1, and the minimum value is -1.

3. Apply the transformations: Apply the vertical stretch/compression and vertical shift to the key points. For this function, the amplitude is 1/2 (which compresses the graph vertically) and the vertical shift is 3 units up.

4. Connect the points: Connect the transformed points smoothly to create the graph of y = (1/2)cos(x) + 3.

5. Optional: Extend the graph to cover the desired interval or domain.

By following these steps, you can graph the function y = (1/2)cos(x) + 3 accurately.