Transforming a function using a parent function

  • Thread starter SwimmingGoat
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In summary, the conversation is about a problem involving a given function and determining if it can be transformed from a known base function. The individual is having trouble finding a suitable parent function and mentions trying the reciprocal but realizing it won't work due to the degree of the numerator. A hint is given to try using long division and the individual expresses gratitude for the help.
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SwimmingGoat
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Ok, I've been working on a long problem (if you want all the steps I've taken to get to this point, I'll give them to you, but they aren't relevant, and I've done them correctly), and now I'm slightly stuck.

Right now I have [tex]f(x)=\frac{x^2+2x}{2x+2}[/tex]. The current problem asks me if the graph can be defined as a transformation of some base function whose graph we already know. I'm having a hard time coming up with a parent function/graph that will help me transform to this equation. Any ideas or thoughts? I thought of doing the reciprocal 1/x, but the degree in the numerator is larger than the denominator...

Thank you in advance!
 
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  • #2
Hi SwimmingGoat! :smile:

Hint: long division? :wink:
 
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  • #3
aha! Thank you! I knew I was missing an obvious place to start. This is what happens when I do math for three hours straight...
 

1. How do I transform a function using a parent function?

To transform a function using a parent function, you can use a set of rules for each type of transformation. These rules involve changing the variables and coefficients in the parent function to create a new function that is transformed from the original.

2. What are the common types of transformations used in transforming a function?

The common types of transformations used in transforming a function include translations, reflections, stretches, and compressions. Other types of transformations include rotations, dilations, and combinations of these transformations.

3. How does a translation affect the graph of a function?

A translation, also known as a shift, involves moving the graph of a function horizontally, vertically, or both. This results in a new graph that is shifted in a certain direction based on the amount of translation applied to the parent function.

4. What is the difference between a reflection and a rotation in transforming a function?

A reflection involves flipping the graph of a function across a line of reflection, while a rotation involves turning the graph of a function around a fixed point. Reflections result in a mirror image of the original graph, while rotations create a new graph with the same shape but different orientation.

5. Can I use multiple transformations on a function at the same time?

Yes, you can use multiple transformations on a function at the same time. This is known as a composition of transformations. It involves applying one transformation after another to the parent function, resulting in a new graph with multiple transformations.

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