Question

Suppose that the graph of f is given. Describe how the graphs of the following functions can be obtained from the graph of f. y=f(x+1/2)

Answer 1

To obtain the graph of y = f(x+1/2) from the graph of f, we need to shift the graph of f horizontally by 1/2 units to the left.

Step-by-step explanation:

To obtain the graph of the function y = f(x+1/2) from the graph of f, we need to shift the graph of f horizontally by 1/2 units to the left. This means that each point on the graph of y = f(x+1/2) will have the x-coordinate shifted 1/2 units to the left compared to the corresponding point on the graph of f.

For example, if the point (2,3) is on the graph of f, then the corresponding point on the graph of y = f(x+1/2) would be (1.5,3).

By applying this horizontal shift to all the points on the graph of f, we can obtain the graph of y = f(x+1/2).