Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x) = \sqrt{x} and g(x) = \sqrt{0.5x}[/tex]

We are told that the following two equations:

f(x) = √x and g(x) = √(0.5x)

And we are asked to find if it's a horizontal or vertical stretch/squeeze.

If you graph both problems (on paper or through a graphing calculator), the answer can be seen. This is how to do it without a graph.

Think of a function as a robot that can do one thing. You ask the robot to take a number, and the robot gives you its square root in f(x). Now in g(x), the robot will take the number and take half of it before the square root.  What happens to our outputs is they made smaller by 1/2 before the square root takes effect. Put another way, our outputs are going to be squeezed faster than before by the inputs. Here, the inputs control the squeezing.

Thus this graph is squeezed horizontally.

slope =   (y2 -y1) ÷ (x2 -x1)

slope = (0 -0) / (-5, -7)

slope = 0 / -12 = 0

the slope of the line is zero.   it is perfectly horizontal.

step-by-step explanation: