Answer to Question #169114 in Algebra for william

Question

In Desmos: Describe the transformations that occurred from the red parent graph f(x)= square root of x to the blue graph.

Answer 1

A vertical stretching is the stretching of the graph away from the x-axis

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis.

• if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k.

• if 0 < k < 1 (a fraction), the graph is f (x) vertically shrunk (or compressed) by multiplying each of its y-coordinates by k.

• if k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.

Notice that the "roots" on the graph stay in their same positions on the x-axis. The graph gets "taffy pulled" up and down from the locking root positions. The y-values change.

if our function is $f(x) = \sqrt{x}$

a) vertical compression/shrink by 1/2$\to$  $kf(x) = \large\frac{\sqrt{x}}{2}$

b) vertical stretch by 2 $\to kf(x) = 2\sqrt{x}$

c) Left 5 $\to f(x + k) = \sqrt{x+5}$

d) Right 5 $\to f(x - k) = \sqrt{x-5}$

e) Up 3 $\to f(x) + k = \sqrt{x} + 3$

f) Down 3 $\to f(x)-k = \sqrt{x} - 3$