Question #167016

In Desmos, choose all transformations being applied too y= 1/23 square root of x+5+3


Select all that apply:

vertical compression/shrink by 1/2

vertical stretch by 2

Left 5

Right 5

Up 3

Down 3


1
Expert's answer
2021-03-09T10:45:59-0500

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

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

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

• if 0 < k < (a fraction), the graph is f (xvertically 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)=xf(x) = \sqrt{x}







a) vertical compression/shrink by 1/2 f(x)=x2f(x) = \large\frac{\sqrt{x}}{2}

b) vertical stretch by 2 f(x)=2xf(x) = 2\sqrt{x}

c) Left 5 f(x+k)=x+5f(x+k) = \sqrt{x+5}

d) Right 5 f(xk)=x5f(x-k) = \sqrt{x-5}

e) Up 3 f(x)=x+3f(x) = \sqrt{x} + 3

f) Down 3 f(x)=x3f(x) = \sqrt{x} - 3




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