How do I perform transformations of functions?

In summary, In general, you need to find x-intercepts, y-intercepts, vertical asymptotes, and horizontal asymptotes. You can also find slant asymptotes by graphing the function and sketching out the graphs.
  • #1
Intr3pid
39
0
hi everyone

I have trouble recognizing expansions/compressions, and not knowing how draw graphs of recipricol transformations (of functions). can someone explain to me how to "do" them? or recommend a site that has a tutorial about it?

thanks in advance.
 
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  • #2
It might help to provide a specific example and explain where/how you are having trouble:smile:
 
  • #3
say f(x) = x^2-5 , how do I graph 1/f(x). Please give an in depth explanation.

thanks in advance
 
  • #4
The easiest way is plot points.
 
  • #5
can anyone give a solution? not just unfinished sentences.
 
  • #6
UnD said:
The easiest way is plot points.

No, in fact that's the hardest way!

Intr3pid said:
say f(x) = x^2-5 , how do I graph 1/f(x)

When graphing rational functions in general, it is best to start by finding the following:

1.) x-intercepts
2.) y-intercepts
3.) Vertical asymptotes
4.) Horizontal asymptotes
5.) Slant asymptotes

Which of these do you know how to find?
 
  • #7
i really need help, i don't get what you guys are saying.
 
  • #8
Intr3pid said:
hi everyone
I have trouble ... not knowing how draw graphs of recipricol transformations (of functions).
What textbook are you using?
Does it have paragraphs "Rational Functions and Asymptotes" and
"Graphs of Rational Functions"?
g(x) = 1/f(x) is a rational function.
 
  • #9
Intr3pid said:
i really need help, i don't get what you guys are saying.

Tom Mattson had it right. You need to look for intercepts and asymptotes. Look at the reciprocal function:

[tex]g(x)=\frac{1}{x^2-5}[/tex]

You need to consider what values of x will cause the function to go to zero, infinity, etc. It's always good to look at limits as x goes to zero and to infinity. You also need to consider what value of x will make the denominator go to zero (meaning what for the value of the function?)
 
  • #10
what I've atleast been told, ad seems to be a fairly easy way to look at it is to call all the x values in the equation y, then all the y values x ( f(x) for ex would be y.. the changed to x ) first of all, then to solve for y -

: the first part i allways found confuzing, and useless at best, so in otherwords just switch around the equation to solve for X after you have named f(x) or f(q) or whatever "Y".

and oh yes- as mentioned above, make sure to disclude answers that will give you nonreal numbers
 

What are the basic types of transformations for functions?

The basic types of transformations for functions include translations, reflections, dilations, and combinations of these. Translations involve shifting the graph of a function horizontally or vertically. Reflections involve flipping the graph of a function across an axis. Dilations involve stretching or compressing the graph of a function. Combinations of these transformations involve applying multiple transformations to a function.

How do transformations affect the graph of a function?

Transformations can change the position, size, and orientation of the graph of a function. They can also affect the domain and range of the function. For example, a horizontal translation shifts the graph left or right, while a vertical dilation stretches or compresses the graph up or down.

What is the difference between a parent function and a transformed function?

A parent function is a basic function that serves as a starting point for transformations. A transformed function is the result of applying one or more transformations to a parent function. For example, the parent function of a linear function is y = x, while the transformed function y = 2x + 3 is the result of applying a translation and a dilation.

How can I determine the equation of a transformed function?

To determine the equation of a transformed function, you can use the general form of the transformation rules for each type of transformation. For example, for a horizontal translation of h units, the equation would be f(x) = f(x - h). For a vertical dilation of a factor of k, the equation would be f(x) = k * f(x). By applying the appropriate transformation rules to the parent function, you can determine the equation of a transformed function.

What is the significance of transformations in real-world applications?

Transformations of functions are important in many real-world applications, such as physics, engineering, and economics. They can be used to model real-world phenomena and make predictions about how they will change over time. For example, transformations of exponential functions can be used to model population growth, and transformations of trigonometric functions can be used to model wave patterns in physics.

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