How do you shift reflect and stretch on 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 do you know if a graph is to the right?
if k > 0, the shift is to the left. if k < 0, the shift is to the right. How to transform a graph vertically? shifts f (x), k units vertically. if k > 0, the shift is upwards. if k < 0, the shift is downwards.
How to stretch shift and reflect the graph of a square root?
Professor ElvisZap teaches you how to stretch shift and reflect the graph of a square root. A square root function is the opposite of a squared function. You start with y=square root of (x-1) it becomes 0<=x-1. then 1 <=x.
How to transform a graph horizontally?
How to transform a graph horizontally? f (x) → f (x + k) shifts f (x), k units horizontally. if k > 0, the shift is to the left.
How do you know if the shift is to the right?
if k > 0, the shift is to the left. if k < 0, the shift is to the right. How to transform a graph vertically? shifts f (x), k units vertically.
How do you shift and reflect a function?
The function translation / transformation rules:f (x) + b shifts the function b units upward.f (x) − b shifts the function b units downward.f (x + b) shifts the function b units to the left.f (x − b) shifts the function b units to the right.−f (x) reflects the function in the x-axis (that is, upside-down).More items...
How do you stretch a function on a graph?
We can also stretch and shrink the graph of a function. To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ).
Do you stretch or reflect graph first?
Scale (Stretch or shrink) Vertical or horizontal order do not matter. Reflect Vertical or horizontal order do not matter. Shift Vertical or horizontal order do not matter.
How do you shift a graph left and right?
The graph of a function can be moved up, down, left, or right by adding to or subtracting from the output or the input. Adding to the output of a function moves the graph up. Subtracting from the output of a function moves the graph down. Here are the graphs of y = f (x), y = f (x) + 2, and y = f (x) - 2.
How do you shift on a graph?
1:1111:09Shifting, Stretching and Reflecting Parent Function Graphs - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf you said shifts right you're right basically the way you want to think about it is whateverMoreIf you said shifts right you're right basically the way you want to think about it is whatever number is grouped with the X is going to shift the graph. Okay in the x-direction.
How do you 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 shift a graph to the left?
In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.
What order do you write transformations?
Apply the transformations in this order:Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.)Deal with multiplication (stretch or compression)Deal with negation (reflection)Deal with addition/subtraction (vertical shift)
What order do u do transformations?
0:347:47Transformation Correct Order - YouTubeYouTubeStart of suggested clipEnd of suggested clipYou can write horizontal translation first and then vertical. Or you can do vertical translationMoreYou can write horizontal translation first and then vertical. Or you can do vertical translation first and then horizontal. And on the other hand you can do vertical stretches.
How do you reflect a graph?
0:367:15Function Transformations: Reflections Across the x-axis and y-axisYouTubeStart of suggested clipEnd of suggested clipIf y equals f of negative x this would reflect f of x about the y axis and here we're changing theMoreIf y equals f of negative x this would reflect f of x about the y axis and here we're changing the sign of the x coordinates and therefore would reflect the graph across the y axis.
How do you stretch a graph horizontally?
3:229:32Function Transformations: Horizontal and Vertical Stretches ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd if we have y equals f of b x where b is between zero and one this will stretch the graph of f ofMoreAnd if we have y equals f of b x where b is between zero and one this will stretch the graph of f of x horizontally.
How do you reflect over the y-axis?
0:101:19How to reflect a point over the y axis - YouTubeYouTubeStart of suggested clipEnd of suggested clipI'm going to be on the left side of the y-axis therefore the x coordinates are now negative so to goMoreI'm going to be on the left side of the y-axis therefore the x coordinates are now negative so to go to X comma Y is now going to be negative X comma Y.
How do you stretch a transformation?
0:005:18Transformations - Veritcal Stretch - Compression - YouTubeYouTubeStart of suggested clipEnd of suggested clipWe're gonna graph the function that has the form y equals K times f of X so some constant times yourMoreWe're gonna graph the function that has the form y equals K times f of X so some constant times your basic function and this is going to be a vertical stretch or compression.
How do you vertically stretch a function?
0:189:32Function Transformations: Horizontal and Vertical Stretches ... - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo if we have y equals a times f of x where a is greater than one this will stretch the graph of fMoreSo if we have y equals a times f of x where a is greater than one this will stretch the graph of f of x vertically by a factor of a.
How do you stretch vertically by a factor of 2?
0:025:00Vertical Stretch by a Factor of 2 Explained - YouTubeYouTubeStart of suggested clipEnd of suggested clipBut notice that the 2 is multiplying the Y values. The x squared gives you the Y value right so theMoreBut notice that the 2 is multiplying the Y values. The x squared gives you the Y value right so the 2 is multiplying those to get you new Y values.
How do you find the stretch factor?
For example, if a function increases three times as fast as its parent function, it has a stretch factor of 3. To find the vertical stretch of a graph, create a function based on its transformation from the parent function, plug in an (x, y) pair from the graph and solve for the value A of the stretch.
What is a shift in math?
Shifts are added/subtracted to the x or f (x) components. If the constant is grouped with the x, then it is a horizontal shift, otherwise it is a vertical shift.
What is a shift in a function?
Shifts. A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged. A horizontal shift adds/subtracts a constant to/from every ...
What is the purpose of translating graphs?
There are some basic graphs that we have seen before. By applying translations to these basic graphs, we are able to obtain new graphs that still have all the properties of the old ones. By understanding the basic graphs and the way translations apply to them, we will recognize each new graph as a small variation in an old one, not as a completely different graph that we have never seen before. Understanding these translations will allow us to quickly recognize and sketch a new function without having to resort to plotting points.
How to reflect a function on the y axis?
A function can be reflected about an axis by multiplying by negative one. To reflect about the y-axis, multiply every x by -1 to get -x. To reflect about the x-axis, multiply f (x) by -1 to get -f (x).
What is translation in which the size and shape of a graph of a function is not changed, but the location?
A translation in which the size and shape of a graph of a function is not changed, but the location of the graph is. Scale. A translation in which the size and shape of the graph of a function is changed. Reflection. A translation in which the graph of a function is mirrored about an axis.
How does translation affect domain and range?
Translations and the Effect on Domain & Range. Any horizontal translation will affect the domain and leave the range unchanged. Any vertical translation will affect the range and the leave the domain unchanged. Apply the same translation to the domain or range that you apply to the x-coordinates or the y-coordinates.
What happens if you memorize every piece of math?
If you were to memorize every piece of mathematics presented to you without making the connection to other parts, you will 1) become frustrated at math and 2) not really understand math.
What is the shift of a shift if k 0?
if k < 0, the shift is to the right.
What is the formula for compressing the graph of f?
y = af (x), 0 < a < 1, will compress the graph of f (x) vertically by a factor of a.
Definitions
Common Functions
Translations
- There are two kinds of translations that we can do to a graph of a function. They are shifting andscaling. There are three if you count reflections, but reflections are just a special case of thesecond translation.
Putting It All Together
- Consider the basic graph of the function: y = f(x) All of the translations can be expressed in the form: y = a * f [ b (x-c) ] + d
Examples
- y=f(x)
1. No translation - y=f(x+2)
1. The +2 is grouped with the x, therefore it is a horizontal translation. Since it is addedto the x, rather than multiplied by the x, it is a shift and not a scale. Since it says plusand the horizontal changes are inversed, the actual translation is to move the entiregraph to the left two units or "s…
Translations and The Effect on Domain & Range
- Any horizontal translation will affect the domain and leave the range unchanged. Any verticaltranslation will affect the range and the leave the domain unchanged. Apply the same translation to the domain or range that you apply to the x-coordinates or the y-coordinates. This works because the domain can be written in interval notation as the intervalbetween two x-coor…
Really Good Stuff
- Understanding the translations can also help when finding the domain and range of a function. Let's say your problem is to find the domain and range of the function y=2-sqrt(x-3). Begin with what you know. You know the basic function is the sqrt(x) and you know the domainand range of the sqrt(x) are both [0,+infinity). You know this because you know those sixcommon functions o…