How do you stretch or shrink a graph?
- When by either f (x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
- In general, a vertical stretch is given by the equation y=bf (x) y = b f ( x ) .
- In general, a horizontal stretch is given by the equation y=f (cx) y = f ( c x ) .
How to stretch or shrink the graph in the x direction?
To stretch or shrink the graph in the x direction, divide or multiply the input by a constant. As in translating, when we change the input, the function changes to compensate. Thus, dividing the input by a constant stretches the function in the x direction, and multiplying the input by a constant shrinks...
How do you shrink a graph by a factor of 3?
If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.
How do you shrink a function in x direction?
Thus, dividing the input by a constant stretches the function in the x direction, and multiplying the input by a constant shrinks the function in the x direction. f (x) is stretched in the x direction by a factor of 2, and f (2x) is shrunk in the x direction by a factor of 2 (or stretched by a factor of frac12 ).
How do you stretch horizontally by a factor of K?
Now let's stretch horizontally by a factor of k. That can be done by replacing x with x/k this time: y = f (x/k) When thought of in that way, the two approaches are the same--only the variable replaced changes depending on if you dilate vertically or horizontally.
How do you stretch and shrink a graph?
0:297:57Pre-Calculus - Applying stretching and shrinking transformations - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf you multiply by a number larger than one on the outside this will stretch it vertically. So itMoreIf you multiply by a number larger than one on the outside this will stretch it vertically. So it makes it look taller in a lot of cases.
How do you know when to stretch or shrink a graph?
2:385:04Vertically Stretching and Shrinking Graphs - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo again we know the graph of something. Then. If you take that real number and multiply it timesMoreSo again we know the graph of something. Then. If you take that real number and multiply it times your original function you're going to get a vertical stretch. If that real if the absolute value of
What does it mean to stretch a graph?
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
How does a graph get stretched?
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.
How do you know if its a horizontal stretch or shrink?
3:159:32Function Transformations: Horizontal and Vertical Stretches ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf we have f of bx where b is greater than one this will compress the graph of f of x horizontally.MoreIf we have f of bx where b is greater than one this will compress the graph of f of x horizontally.
How do you find a horizontal stretch or shrink?
A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x). Consider the following base functions, (1) f (x) = x2 - 3, (2) g(x) = cos (x).
What is a shrink in math?
Also, a vertical stretch/shrink by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x).
What is a transformation that shrinks or stretches a figure?
Dilation. a transformation that shrinks or stretches a figure.
How do you compress and stretch a function?
In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
How do you shrink a graph horizontally?
To shrink or compress horizontally by a factor of c, replace y = f(x) with y = f(cx). Note that if |c|<1, that's the same as scaling, or stretching, by a factor of 1/c.
How do you stretch a horizontal graph?
We can only horizontally stretch a graph by a factor of 1/a when the input value is also increased by a. When f(x) is stretched horizontally to f(ax), multiply the x-coordinates by a. Retain the y-intercepts' position. The resulting function will have the same range but may have a different domain.
What is a stretch in math?
A stretch or compression is a function transformation that makes a graph narrower or wider. stretching. Stretching a graph means to make the graph narrower or wider.
Translating (shifting) a graph
Translation means moving an object without rotation, and can be described as “sliding”. In describing transformations of graphs, some textbooks use the formal term “translate”, while others use an informal term like “shift”.
A note on reflection
None of these discussions went deeper into reflections than a brief mention in the first question. I will just add here that you can think of a reflection as a “stretch by a factor of -1”. That is, it just reverses direction.
Horizontal shifts: A closer look
The horizontal transformations, involving x, confuse many students. Here is a question from 2002 about just that:
Horizontal stretches
In general, everything we do with x will be the opposite of what you might expect, for this same reason. This is true not only of horizontal shifts, but of horizontal stretching as well, which we haven’t seen yet. Here is a question specifically about that issue, from 2004:
Why horizontal transformations are backward
Functional Transformations Explained and Undone Why do horizontal transformations behave in an opposite manner? For example, why does f (x + c) shift a graph c units to the left? Likewise, to shrink or stretch horizontally, i.e., f (cx), why do you divide the x coordinate by c?
What do you call it?
Stretching Definitions, and Compressing The original function is y = f (x). Given a new function y = f (cx).
Translating (Shifting) A Graph
Shifting and Stretching
- Here is another very similar question from 2001: This time we have a vertical translation, a horizontal translation, and a vertical dilation. I chose to illustrate each concept with sample graphs, with only brief explanation of why they do what they do: Here are some actual graphs corresponding to the three above: [shift up 2]: Here, the point (2, ...
A Note on Reflection
- None of these discussions went deeper into reflections than a brief mention in the first question. I will just add here that you can think of a reflection as a “stretch by a factor of -1”. That is, it just reverses direction. So a vertical reflection (reflection in the x-axis) is accomplished by , which changes the sign of y; and a horizontal reflection (reflection in the y-axis) is accomplished by , w…
Horizontal Shifts: A Closer Look
- The horizontal transformations, involving x, confuse many students. Here is a question from 2002 about just that: I referred to the last answer, and gave a little more detail: We have to add c to x to compensate for the fact that it will be decreased by c before being fed into function f. So replacing with in the function moves every point to the right by cunits.
Horizontal Stretches
- In general, everything we do with xwill be the opposite of what you might expect, for this same reason. This is true not only of horizontal shifts, but of horizontal stretching as well, which we haven’t seen yet. Here is a question specifically about that issue, from 2004: Here is an example, based on our function above: The dotted graph is f(2x), compressed (shrunk) by a factor of 1/2 h…
What Do You Call It?
- In 2014, we got a very different question, asking about the terminology of stretches: If you don’t see what Jason is concerned about, notice that for , his book calls it a stretch by a factor of , where I would call it 2; and it calls f(2x) a compression by a factor of 2, which could also be called a factor of (since that is what coordinates are multiplied by). Is the book wrong? I had observed …