Transforming Graphs

Transformation of graphs​

translation, stretching and reflection

instruction

Mathematics | Transformation of graphs

instruction

Mathematics | Transformation of graphs

instruction

After inputting the f(x), it will be our original function.

​

Move the sliders to apply any changes.

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We firstly change ​the values of h and k only.

Observe clearly the "transformation" applied on the original ​curve.

Mathematics | Transformation of graphs

instruction

You may play with the applet for a while and answer the question afterwards.

Mathematics | Transformation of graphs

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​Answer the following questions

Multiple Choice

Describe the transformation

$$f\left(x\right)+3$$  

• 3 Units Up

• 3 Units Down

• 3 Units Left

• 3 Units Right

Multiple Choice

Describe the transformation

$$f\left(x-2\right)$$  

• 2 Units Up

• 2 Units Down

• 2 Units Left

• 2 Units Right

Multiple Choice

Describe the transformation

$$f\left(x+5\right)$$  

• 5 Units Up

• 5 Units Down

• 5 Units Left

• 5 Units Right

Multiple Choice

Describe the transformation

$$f\left(x\right)-6$$  

• 6 Units Up

• 6 Units Down

• 6 Units Left

• 6 Units Right

instruction

If you answer the previous questions correctly, you may try to change the values of a or b then.

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You are suggested to change only a or b at each time, and keep the other values as default.

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-If we make a=3, keep b=1, h=0 and k=0. Or press reset before changes

Mathematics | Transformation of graphs

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​Answer the following questions

Multiple Choice

Describe the transformation

$$3h\left(x\right)$$  

• Vertically Stretched by a factor of 3

• Vertically Stretched by a factor of $$\frac{1}{3}$$  

• Horizontally Stretched by a factor of 3

• Horizontally Stretched by a factor of $$\frac{1}{3}$$  

Multiple Choice

Describe the transformation

$$h\left(\frac{1}{3}x\right)$$  

• Vertically Stretched by a factor of $$\frac{1}{3}$$  

• Vertically Stretched by a factor of $$3$$  

• Horizontally Stretched by a factor of $$\frac{1}{3}$$  

• Horizontally Stretched by a factor of $$3$$  

instruction

If you answer the previous questions correctly, you may try to change more than one variable at each time.

​

While you are playing with the applet, please be reminded to observe what have been changed and ​what is the order of the changes on f(x) to become g(x).

Mathematics | Transformation of graphs

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​Answer the following questions (mixed transformation)

Multiple Choice

Describe the transformations

$$-g\left(x\right)+2$$  

• Reflected in the x-axis

  2 Units Up

• Reflected in the x-axis

  2 Units Down

• Reflected in the y-axis

  2 Units Up

• Reflected in the y-axis

  2 Units Down

Multiple Choice

Describe the transformations

$$g\left(-x\right)-4$$  

• Reflected in the x-axis

  4 Units Left

• Reflected in the x-axis

  4 Units Down

• Reflected in the y-axis

  4 Units Left

• Reflected in the y-axis

  4 Units Down

Multiple Choice

Given the parent exponential function y=4^x,

how would the graph change if the function were:

y=2(4)^x-3+1?

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically stretched by a factor of 1/2, left 3 and down 1

• Vertically stretched by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

Multiple Choice

What equation would yield a transformation right 3 units if your initial function was y=2^x

• y=2^x-3
• y=2^x+3
• y=2^x+3
• y=2^x-3

Multiple Choice

compare with $$y=\sqrt[]{x}$$ , the graph of  $$y=-\sqrt[]{-x+2}-3$$  has been...

• This graph has been reflected in the x-axis and y-axis, shifted to the left two units, and shifted down three units.

• This graph has been reflected in the y-axis, shifted to the right by two units, and shifted down three units.

• This graph has been reflected in the x-axis and y-axis, shifted to the left two units, and shifted up three units.

• This graph has been reflected in the x-axis and y-axis, shifted to the right two units, and shifted down three units.

Multiple Choice

This is an absolute value function $$y=\left|x\right|$$  . It has been stretched vertically by a factor of eleven, shifted to the right by two units, and shifted up by four units.

• $$y=\left|11x+2\right|-4$$

• $$y=\left|x\right|$$  

• $$y=11\left|x-2\right|+4$$  

• $$y=11\left|x+2\right|+4$$

​let's us conclude our observation

Multiple Choice

What transformation is f(x)+d

• Vertical translation by d units up

• Vertical ranslation by d units down

• Horizontal translation by d units left

• Horizontal translation by d units right

Multiple Choice

What transformation is f(x)-d

• Vertical translation by d units up

• Vertical translation by d units down

• Horizontal translation by d units left

• Horizontal translation by d units right

Multiple Choice

What transformation is f(x+c)

• Translation in y direction by c units up

• Translation in y direction by c units down

• Translation in x direction by c units left

• Translation in x direction by c units right

Multiple Choice

What transformation is f(x-c)

• Translation in y direction by c units up

• Translation in y direction by c units down

• Translation in x direction by c units left

• Translation in x direction by c units right

Multiple Choice

What transformation is -f(x)

• Reflection in the

  y-axis

• Reflection in the

  x- axis

• Translation in y direction

• Translation in x direction

Multiple Choice

What transformation is f(-x)

• Reflection in the

  y-axis

• Reflection in the

  x-axis

• Translation in the y direction

• Translation in the x direction

Multiple Choice

What transformation is af(x)

• Stretch in y direction by scale factor a

• Stretch in y direction by scale factor 1/a

• Stretch in x direction by scale factor a

• Stretch in x direction by scale factor 1/a

Multiple Choice

What transformation is f(bx)

• Stretch in y direction by scale factor b

• Stretch in y direction by scale factor 1/b

• Stretch in x direction by scale factor b

• Stretch in x direction by scale factor 1/b