Transformations of Square Root Functions

Presentation

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Mathematics

•

9th Grade - University

•

Practice Problem

•

Medium

•

CCSS

HSF.BF.B.3, HSF-IF.C.7B

Standards-aligned

Monta Jeffley

Used 23+ times

FREE Resource

8 Slides • 27 Questions

Transformations of Square Root Functions

By Monta Jeffley

This is the square root function in a more complex form, it will help you understand how the graph moves through the coordinate plane.

Square Root Function

If the "a" is negative, you will reflect over the x-axis.

If the "b" is negative, you will reflect over the y-axis.

Reflections

Multiple Choice

Describe the transformation for:

$-2\ \sqrt[]{x}$

Reflection over the x-axis

Reflection over the y-axis

Multiple Choice

Describe the transformation for:

$\ \sqrt[]{-5\ x}$

Reflection over the x-axis

Reflection over the y-axis

Multiple Choice

Describe the transformation for:

$\ -6\ \sqrt[]{x\ +\ 3}\ -\ 6$

Reflection over the x-axis

Reflection over the y-axis

Multiple Choice

Describe the transformation for:

$\ \sqrt[]{-2x\ +\ 4}\ +\ 7$

Reflection over the x-axis

Reflection over the y-axis

Multiple Select

Describe the transformation for:

$\ -\frac{2}{3}\sqrt[]{-x\ -\ 5}\ -\ 2$

Reflection over the x-axis

Reflection over the y-axis

The letter "a" controls the vertical compression and stretch of a graph.

-If a > 1, it is a vertical stretch

-If 0<a<1 (a is between 0 and 1), it is a vertical compression. 

Vertical Compressions and Stretches

Multiple Choice

Describe the transformation for:

$\frac{1}{3}\ \sqrt[]{x}$

Vertical Stretch

Vertical Compression

Multiple Choice

Describe the transformation for:

$6\ \sqrt[]{x}$

Vertical Stretch

Vertical Compression

Multiple Choice

Describe the transformation for:

$-\frac{5}{4}\ \sqrt[]{3x}\ +\ 3$

Vertical Stretch

Vertical Compression

Multiple Choice

Describe the transformation for:

$\frac{2}{3}\ \sqrt[]{-2x}\ -\ 13$

Vertical Stretch

Vertical Compression

The letter "b" controls the horizontal compression and stretch of a graph.

-If b > 1, it is a horizontal compression

-If 0<b<1 (a is between 0 and 1), it is a horizontal stretch.

Horizontal Compressions and Stretches

Multiple Choice

Describe the transformation for:

$\ \sqrt[]{2x}$

Horizontal Stretch

Horizontal Compression

Multiple Choice

Describe the transformation for:

$\ \sqrt[]{\frac{3}{4}x}$

Horizontal Stretch

Horizontal Compression

Multiple Choice

Describe the transformation for:

$-\ \sqrt[]{\frac{1}{8}x\ -4}\ +\ 7$

Horizontal Stretch

Horizontal Compression

Multiple Choice

Describe the transformation for:

$5\ \sqrt[]{3x\ +\ 6}\ -\ 1$

Horizontal Stretch

Horizontal Compression

The letter "c" controls the horizontal shift of a graph.

Remember, to move the opposite direction of what you see.

-If you see "+ c" move left.

-If you see "- c" move right.

Horizontal Shifts (moving left and right)

This number is underneath the square root and behind the x.

Multiple Choice

Describe the transformation for:

$\sqrt[]{x\ +\ 6}$

Shift right 6 units

Shift left 6 units

Multiple Choice

Describe the transformation for:

$\sqrt[]{x\ -\ 10}$

Shift right 10 units

Shift left 10 units

Multiple Choice

Describe the transformation for:

$3\ \sqrt[]{2x\ -\ 1}\ +\ 5$

Shift right 1 unit

Shift left 1 unit

Shift left 5 units

Shift right 5 units

Multiple Choice

Describe the transformation for:

$-\frac{3}{4}\ \sqrt[]{x\ +\ 9}\ -\ 4\$

Shift right 4 units

Shift left 9 units

Shift left 4 units

Shift right 9 units

The letter "d" controls the vertical shift of a graph.

-If you see "+ d" move up.

-If you see "- d" move down.

Vertical Shifts (moving up and down)

This number is added to or subtracted from the square root symbol. It is NOT underneath the square root.

Multiple Choice

Describe the transformation for:

$\sqrt[]{x\ }\ -\ 4\$

Shift down 4 units

Shift up 4 units

Multiple Choice

Describe the transformation for:

$\sqrt[]{x\ }+\ 3$

Shift up 3 units

Shift down 3 units

Multiple Choice

Describe the transformation for:

$-4\ \sqrt[]{\frac{1}{2}x\ -4\ }+\ 6$

Shift up 4 units

Shift down 4 units

Shift down 6 units

Shift up 6 units

Multiple Choice

Describe the transformation for:

$\frac{4}{5}\ \sqrt[]{8x\ +\ 5\ }-\ 2$

Shift up 8 units

Shift down 5 units

Shift down 2 units

Shift up 2 units

Mixed Practice

Read each question carefully, and select the correct answer. USE YOUR NOTES IF YOU NEED THEM!

Multiple Select

SELECT ALL THAT APPLY for the transformations that best describe this graph:

$f\left(x\right)\ =\ -2\ \sqrt[]{x}\ +\ 4\$

Reflection over the x-axis

Reflection over the y-axis

Horizontal Compression

Vertical Stretch

Vertical Shift

$\uparrow\ or\ \downarrow$

Multiple Select

SELECT ALL THAT APPLY for the transformations that best describe this graph:

$f\left(x\right)\ =\ \sqrt[]{-\frac{2}{5}x\ -\ 3}\$

Reflection over the x-axis

Reflection over the y-axis

Horizontal Stretch

Vertical Compression

Horizontal Shift

$\longleftarrow\ or\ \longrightarrow$

Multiple Choice

Which equation best represents the graph?

$f\left(x\right)\ =\ \sqrt[]{x\ }+\ 1$

$f\left(x\right)\ =\ \sqrt[]{x}\ -\ 1$

$f\left(x\right)\ =\ \sqrt[]{x\ +\ 1}$

$f\left(x\right)\ =\ \sqrt[]{x\ -\ 1}$

Multiple Choice

Which equation best represents the graph?

$f\left(x\right)\ =\ \sqrt[]{x\ }+\ 3$

$f\left(x\right)\ =\ \sqrt[]{x}\ -\ 3$

$f\left(x\right)\ =\ \sqrt[]{x\ +\ 3}$

$f\left(x\right)\ =\ \sqrt[]{x\ -\ 3}$

Multiple Choice

Which equation would be:

-Reflected over the y-axis

-Compressed horizontally by 4

-Shifted left 10 units

-Shifted down 9 units

$f\left(x\right)\ =\ -4\ \sqrt[]{x\ +10\ }-\ 9$

$f\left(x\right)\ =\ \sqrt[]{-4x\ +\ 10}\ -\ 9$

$f\left(x\right)\ =\ -\ \sqrt[]{4x\ +\ 10}\ -\ 9$

$f\left(x\right)\ =\ \sqrt[]{-4x\ -\ 10}\ -\ 9$

Multiple Choice

Which equation would be:

-Compressed vertically by 1/2

-Stretched horizontally by 2/3

-Shifted right 7 units

-Shifted up 4 units

$f\left(x\right)\ =\ \frac{2}{3}\ \sqrt[]{\frac{1}{2}x\ -\ 7\ }+\ 4$

$f\left(x\right)\ =\ \frac{2}{3}\ \sqrt[]{\frac{1}{2}x\ +\ 7}\ +\ 4_{ }$

$f\left(x\right)\ =\ \frac{1}{2}\ \sqrt[\ ]{\frac{2}{3}x\ -\ 7}\ +\ 4$

$f\left(x\right)\ =\ \frac{1}{2}\ \sqrt[]{\frac{2}{3}x\ +\ 7}\ +\ 4$

Transformations of Square Root Functions

By Monta Jeffley

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