Transforming Piecewise Functions

In summary, the piecewise function -x-2 for x<-1, x^2-3x for -1≤x≤5, and 3x+5 for x>5 is being transformed by reflecting the function in the x-axis, horizontally stretching it by a factor of 6, translating it left 3 units, and vertically stretching it by a factor of 4. These transformations result in the new function ((2x)/3)+20 for x<12, ((-2x^2)/3)+12 for 12≤x≤48, and -2x-8 for x>48. The border x=-1 remains the same when reflected in the x-axis, but is
  • #1
Mjucewitz

Homework Statement


The piece wise function is
-x-2, x<-1
x^2-3x, -1≤ x ≤5
3x+5, x>5
The problem is to transform the function with these series of transformations
  • reflection in the x-axis
  • Horizontal stretch by a factor of 6
  • Translation left 3 units
  • Vertical Stretch by a factor of 4

Homework Equations


The basic transformation rules for a function

The Attempt at a Solution


I was able to transform the function part, but I can not figure out how the domain is suppose to be affected by the transformations. All I have is
((2x)/3) + 20
(((-2x^2)/3)+12) + (2x+3)
-2x-8
Update: I tried my best at the domain and got:
x<12
12≤x≤48
x>48
 
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  • #2
One of the borders is x=-1. What happens if you reflect this border at the x-axis, or do one of the other operations?
 
  • #3
mfb said:
One of the borders is x=-1. What happens if you reflect this border at the x-axis, or do one of the other operations?
If you were to reflect the border x = -1 over the x-axis would it not stay the same?
 
  • #4
Right.
What happens with the other operations?
 

1. What is a piecewise function?

A piecewise function is a mathematical function that is defined by different equations for different intervals of the independent variable. This means that the function is not defined by a single equation, but rather by multiple equations that are used depending on the value of the independent variable.

2. How do you transform a piecewise function?

To transform a piecewise function, you can apply transformations to each individual equation within the function. This can include translations, reflections, stretches, or compressions. It is important to make sure that the transformations are applied consistently to all equations within the function.

3. What are some common transformations used in transforming piecewise functions?

Some common transformations used in transforming piecewise functions include changing the slope or intercept of a linear equation, changing the x-value or amplitude of a trigonometric function, and changing the degree or coefficients of a polynomial function.

4. How do you graph a transformed piecewise function?

To graph a transformed piecewise function, you can graph each individual equation separately and then combine them to create the overall graph of the function. It is important to correctly label each interval and to make sure that the transformations are accurately reflected in the graph.

5. What is the purpose of transforming a piecewise function?

The purpose of transforming a piecewise function is to modify the original function in order to better fit a specific scenario or to make it easier to work with mathematically. Transforming can also help to visualize the behavior of the function and make predictions about its output.

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