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Graphical Transformations. Vertical and Horizontal Translations Vertical and Horizontal Stretches and Shrinks. Take the equation f(x)= x 2. How do you modify the equation to translate the graph of this equation 5 units to the right?........ 5 units to the left?

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graphical transformations

Graphical Transformations

Vertical and Horizontal Translations

Vertical and Horizontal Stretches and Shrinks

take the equation f x x 2
Take the equation f(x)= x2
  • How do you modify the equation to translate the graph of this equation 5 units to the right?........ 5 units to the left?
  • How do you modify the equation to translate the graph of this equation 3 units down?..............3 units up?
  • What if you wanted to translate the graph of this equation 5 units to the left and 3 units down?
slide3

The parabola has been translated 5 units to the right.

How is the equation modified to cause this translation?

slide4

Notice the change in the equation y = x2 to create the horizontal

shift of 5 units to the right.

f(x) = x2

g(x) = (x-5)2

slide5

The parabola is now translated 5 units to the left.

How is the equation modified to cause this translation?

slide6

Notice the change in the graph of the equation y=x2 to

create a horizontal shift of 5 units to the left.

f(x)=x2

h(x)=(x+5)2

slide7

The parabola has now been translated three units down.

How is the equation modified to cause this translation?

slide8

Notice how the equation y = x2 has changed to make the

Vertical translation of 3 units down.

f(x)=x2

q(x)=x2-3

slide9

The parabola has now been translated 3 units up.

How is the equation modified to cause this translation?

slide10

Notice how the equation y = x2 has been changed to make the

Vertical translation 3 units up.

f(x)=x2

r(x)=x2+3

slide11

Write what you think would be the equation for translating

the parabola 5 units to the left and 3 units up?

slide12

The equation would be

What would the graph would look like?

vertical and horizontal stretches and shrinks
Vertical and horizontal stretches and shrinks
  • How does the coefficient on the x2 term affect the graph of f(x) = x2?
  • What if we substitute an expression such as 2x into f(x)? How would that affect the graph of f(x) = x2?
slide15

The parabola has been vertically stretched by a factor of 2.

Notice how the equation has been modified to cause this stretch.

slide16

The parabola is vertically shrunk by a factor of ½.

Notice how the equation has been modified to cause this shrink.

slide17

By substituting an expression like 2x in for x in f(x) = x2

gives a different type of shrink. f(2x) = (2x)2. A horizontal

shrink by a factor of ½.

slide18

Suppose we found g(1/2x). The equation would be

y = (1/2x)2.. How would this affect the graph of the

function g(x) = x2? It is a horizontal stretch by a factor

of 2.

slide19

If we were to write some rules for translations of functions

and stretches/shrinks of functions, what would we write?

Horizontal translation:

Vertical translation:

Vertical stretch:

Vertical shrink:

Horizontal stretch:

Horizontal shrink: