Introduction to Geometry and Tranformations

[Thejonster101]

1. Write functions for the followingtransformations using function notation. Choose a different letter to representeach function. For example, you can use Rto represent rotations. Assume that a positive rotation occurs in thecounterclockwise direction.

• translationof a units to the right and b units up
  
• reflectionacross the y-axis
  
• reflectionacross the x-axis
  
• rotationof 90 degrees counterclockwise about the origin, point O
  
• rotationof 180 degrees counterclockwise about the origin, point O
  
• rotationof 270 degrees counterclockwise about the origin, point O
  
  If someone could give the answers and explain how to do it that would be amazing! thanks
  
  

 

[mmm4444bot]

[please] give the answers and explain how to do it

that would be amazing

Please explain the parts where you're stuck, showing any work thus far.

Do you understand the meaning of the first one?

If not, we would like to know the following. Do you need links to lessons (i.e., you're self-studying), or are there any issues with your course materials? Do you know how to graph lines in the xy-plane (linear functions)? Do you understand what function notation is? Your answers will help us determine how to proceed.

Please also check out the forum guidelines. Here's a link to the summary page.

Thank you! :cool:

 

[Quaid]

Write functions for the following transformations using function notation. Choose a different letter to represent each function

• translation of a units to the right and b units up

Graph the following two functions. What is the difference between the two graphs?

f(x) = sin(x)

g(x) = sin(x) + 1

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Graph the following two functions. What is the difference between the two graphs?

u(x) = sin(x)

v(x) = sin(x - 1)

 

[Quaid]

Graph the following two functions. What is the difference between the two graphs?

f(x) = sin(x)

g(x) = sin(x) + 1

Entering sin(x) into Google displays a graph. When we enter sin(x) + 1, we see the graph of sin(x) shifted up one unit.

Graphing sin(x) + 2 shows the graph of sin(x) shifted up 2 units.

If we add a positive constant to a function's output, it causes the function's graph to shift up by the same amount. Adding a negative constant causes a shift down.

The translation of f(x) up C units is f(x) + C, where C is greater than zero.

To show function f shifted up b units, we need to state that symbol b represents a positive number and then add b to the function's output.

b > 0

f(x) + b

Graph the following two functions. What is the difference between the two graphs?

u(x) = sin(x)

v(x) = sin(x - 1)

Googling graphs for sin(x), sin(x-1), and sin(x-2) shows that subtracting a positive amount from a function's input causes the graph to shift to the right; the graph of sin(x-1) is shifted one unit to the right of sin(x).

The translation of f(x) to the right C units is f(x - c), where C is greater than zero.

To show function f shifted to the right a units, we need to state that symbol a represents a positive number and then subtract a from the function's input.

a > 0

f(x - a)

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Combining the concepts above, answers the first question. Translate f(x) to the right a units and up b units.

a > 0

b > 0

f(x - a) + b