Horizontal Stretches Open the horizontal stretch apple.

(a) Use your mouse to grab the slider and change the value of a. Note the role a plays in the graph of g(x) = f(ax) = √ax, where f(x) = √x. What happens to the points on the graph of g when 0 < a < 1? What happens to the points on the graph when a > 1?

(b) To further understand the concept of horizontal compressions, fill in the spreadsheet to the right of the graph as follows:

(i) What x-coordinate is required on the graph of g(x) = √2x, if the y-coordinate is to be 1?

(ii) What x-coordinate is required on the graph of g(x) = √2x if the y-coordinate is to be 2?

(iii) What x-coordinate is required on the graph of g(x) = √2x, if the y-coordinate is to be 3?

(iv) What x-coordinate is required on the graph of g(x) = √1/2 x, if they-coordinate is to be 1?

(v) What x-coordinate is required on the graph of g(x) = √1/2x, if they-coordinate is to be 2?

(vi) What x-coordinate is required on the graph of g(x) = √1/2x, if they-coordinate is to be 3?