Suppose the graph of f is given Describe how the graph of ea

Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph of f. (a) -f(x) reflect about the y-axis reflect about the x-axis reflect about the origin shift to the left by 1 unit shift to the right by 1 unit (b) 1/6f(x) reflect about the y-axis reflect about the x-axis reflect about the origin shrink vertically by 1/6 stretch vertically by 1/6

Solution

(a) The graph of –f(x) can be obtained from the graph of f(x)by reflecting about the X-Axis. The 2^nd option is the correct answer.

(b) Multiplying a function by a constant greater than 1 has the effect of stretching the graph vertically.Also, the graph of y 5 cf(x) is a vertical compression toward the x-axis if c < 1. The graph of (1/6)f(x) can be obtained from the graph of f(x)by stretching vertically by 1/6. The last option is the correct answer. ( Shrinking to 1/6 is same as stretching by 1/6).