Sketch the graph of the given equation over the interval [-2π, 2π]
y=sinx+5
Select.all the transformations that are needed to graph the given function using y=sinx. And show your work or explain why for each transformation.
A. Stretch the graph vertically.
B. Reflect the graph about the y-axis.
C. Shift the graph to the left 5 units.
D. Stretch the graph horizontally.
E. Shift the graph up 5 units
F. Shift the graph down 5 units.
G. Reflect the graph about the x axis.
H. Shift the graph to the right 5 units
I. Compress the graph vertically.
J. Compress the graph horizontally.
The equation y = sin(x) represents the standard sine function. Let's go through each transformation option and determine if it is needed or not, and explain why.
A. Stretch the graph vertically:
This transformation is not needed because there is no coefficient multiplying the sine function. The coefficient is 1, which means the graph remains the same vertical size.
B. Reflect the graph about the y-axis:
This transformation is not needed because the graph remains the same orientation.
C. Shift the graph to the left 5 units:
This transformation is not needed to graph y = sin(x) + 5. The function y = sin(x) + 5 shifts the graph vertically, not horizontally.
D. Stretch the graph horizontally:
This transformation is not needed because there is no coefficient affecting the x variable. The graph remains the same horizontally.
E. Shift the graph up 5 units:
This transformation is needed because the equation y = sin(x) + 5 shifts the graph up by 5 units.
F. Shift the graph down 5 units:
This transformation is not needed because y = sin(x) + 5 already shifts the graph up by 5 units.
G. Reflect the graph about the x-axis:
This transformation is not needed because the graph remains the same orientation.
H. Shift the graph to the right 5 units:
This transformation is not needed to graph y = sin(x) + 5. The function y = sin(x) + 5 shifts the graph vertically, not horizontally.
I. Compress the graph vertically:
This transformation is not needed because there is no coefficient affecting the y variable. The graph remains the same vertical size.
J. Compress the graph horizontally:
This transformation is not needed because there is no coefficient affecting the x variable. The graph remains the same horizontally.
Therefore, the necessary transformations to graph y = sin(x) + 5 are:
- Shift the graph up 5 units.
Please note that these transformations are specific to the graph of y = sin(x) + 5, not the standard sine function y = sin(x).