What is a vertical stretch in math definition?
- 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 calculate vertical stretch?
Vertical Stretches To stretch a graph vertically, place a coefficient in front of the function. This coefficient is the amplitude of the function. For example, the amplitude of y = f (x) = sin(x) is one. The amplitude of y = f (x) = 3 sin(x) is three. Compare the two graphs below.
What is horizontal stretch in mathematics?
This is what happens to the points:
- (-3, 9) → (-9, 9)
- (-2, 4) → (-6, 4)
- (-1, 1) → (-3, 1)
- (0, 0) → (0, 0)
- (1, 1) → (3, 1)
- (2, 4) → (6, 4)
- (3, 9) → (9, 9)
What is the difference between horizontal and vertical stretch?
In this video we discuss the effects on the parent function when:
- Stretched Vertically,
- Compressed Vertically,
- Stretched Horizontally,
- Compressed Horizontally.
What does a vertical stretch look like?
What does a vertical stretch look like on a graph? Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. This results in the graph being pulled outward but retaining the input values (or x). When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis.
What is a vertical stretch example?
2:385:05Vertically Stretching and Shrinking Graphs - YouTubeYouTubeStart of suggested clipEnd of suggested clipIf you take that real number and multiply it times your original function you're going to get aMoreIf 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 that real number is greater than 1.
What is a horizontal stretch in math?
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). Examples of Horizontal Stretches and Shrinks.
Why is it called a vertical stretch?
The y -values are being multiplied by a number greater than 1 , so they move farther from the x -axis. This tends to make the graph steeper, and is called a vertical stretch.19-Apr-2021
How do you stretch vertically?
0:222:02How to do a vertical stretch - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo simply put you take this put where this is so that's one-third X minus 2. And then you put thisMoreSo simply put you take this put where this is so that's one-third X minus 2. And then you put this number where that a is so be three okay you just multiply it in there chill.
What is vertical and horizontal?
Horizontal is the opposite of vertical. ... As vertical is the opposite of horizontal, anything that makes a 90-degree angle (right angle) with the horizontal or the horizon is called vertical. So, the horizontal line is one that runs across from left to right.
What is vertical stretch and shrink?
A vertical stretching is the stretching of the graph away from the x-axis. A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis.
What does vertically stretched by a factor of 2 mean?
Stretching f(x) vertically by a factor of 2 will result in h(x) being equal to 2 times f(x). Stretching f(x) vertically by a factor of 3 will result to h(x) being equal to 3 times f(x).
How do you tell if a graph is vertically 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.
Is vertical stretch and horizontal compression the same?
1:2614:12Horizontal and Vertical Stretch and Compression - YouTubeYouTubeStart of suggested clipEnd of suggested clipWhen we are between 0 & 1. So the compression and stretch are opposite of the way it was with theMoreWhen we are between 0 & 1. So the compression and stretch are opposite of the way it was with the horizontal. Okay so horizontal compression occurs when we're multiplying inside the parentheses.
Does vertical stretch get wider?
0:039:33Horizontal and Vertical Stretches and Compressions - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo if we have y equals a times f of X where a is greater than 1 this will stretch the graph of f ofMoreSo if we have y equals a times f of X where a is greater than 1 this will stretch the graph of f of X vertically by a factor of a.
How do you vertically stretch a quadratic equation?
0:526:24Vertical Stretch or Compression of a Quadratic Function - YouTubeYouTubeStart of suggested clipEnd of suggested clipAnd if it's more than one that it's going to do the vertical stretch. So it has to be between 0 andMoreAnd if it's more than one that it's going to do the vertical stretch. So it has to be between 0 and 1 like 1/2 or 1/3 1/4. Two-fifths any fraction that is between 0 and 1 or decimal.
Function Transformations: Horizontal And Vertical Translations
This video explains to graph graph horizontal and vertical translation in the form af (b (x-c))+d. It looks at how c and d affect the graph of f (x).
Function Transformations: Horizontal And Vertical Stretch And Compression
This video explains to graph graph horizontal and vertical stretches and compressions in the form af (b (x-c))+d. It looks at how a and b affect the graph of f (x).
Horizontal And Vertical Graph Stretches And Compressions (Part 2)
This video discusses the horizontal stretching and compressing of graphs.
Graph Transformations About The X-Axis And Y-Axis
This video talks about reflections around the X axis and Y axis. (Part 3)
Different Types Of Math Transformation
There are different types of math transformation, one of which is the type y = f (bx). This type of math transformation is a horizontal compression when b is greater than one. We can graph this math transformation by using tables to transform the original elementary function.
How to compress a function?
To vertically compress a function, multiply the entire function by some number less than 1. This is the opposite of vertical stretching: whatever you would ordinarily get out of the function, you multiply it by 1/2 or 1/3 or 1/4 to get the new, smaller y -value. That's great, but how do you know how much you're stretching or compressing ...
How to stretch a function?
To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
What does vertical stretching mean?
Vertical stretching means making the y -value bigger for any given value of x, and you can do it by multiplying the entire function by something greater than 1. Vertical compression means making the y -value smaller for any given value of x, and you can do it by multiplying the entire function by something less than 1.
What does horizontal compression mean?
Horizontal compression means making the x -value smaller for any given value of y, and you can do it by multiplying x by something more than 1 before any other operation. To unlock this lesson you must be a Study.com Member. Create your account.
Can you multiply x by 1/2?
Well, you could change the function to multiply x by 1/2 before doing any other operations, so that you can plug in 10 where you used to have 5 and get the same value for y at the end. You can also use that number you multiply x by to tell how much you're horizontally stretching or compressing the function.
What is vertical alignment?
A vertical is an alignment in which the top is always above the bottom. It is a property of two or more points in which if a point is directly below the second point, and they are vertical to each other.
Is a perpendicular line horizontal or vertical?
Although horizontal and vertical lines are perpendicular, all perpendicular lines are not horizontal or vertical. For example, the Leaning Tower of Pisa, the pillars of the tower are perpendicular to the floor but are not vertical. Won Numerous Awards & Honors.
Is a line or object that is moving upright or downright vertical?
So any line or object that is moving upright or downright is vertical. Given below are some examples of vertical: A different way of looking at vertical is through horizontal. Vertical lines or objects are always perpendicular to the horizontal lines or objects. Some examples are shown below:
Is a line parallel to the y axis a vertical line?
In math, the y-axis is considered vertical. Hence any line parallel to the y-axis is a vertical line. Also, vertical lines are perpendicular to the x-axis. Given below are some examples. Line L in the given picture is vertical as it is parallel to the y-axis.
