What is compression and stretch?

Asked By: Whitley Dzhabrailov | Last Updated: 21st February, 2020
Category: science space and astronomy
4.3/5 (35 Views . 23 Votes)
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.

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Furthermore, what is the difference between vertical stretch and compression?

Vertical stretching means the function is stretched out vertically, so it's taller. Vertical compression means the function is squished down vertically, so it's shorter. On the graph of a function, the F(x), or output values of the function, are plotted on the y-axis.

Furthermore, what is a compression in math? A compression occurs when a mathematical object is scaled by a scale factor less in absolute value than one. When a compression occurs, the image is smaller than the original mathematical object. If the scaling occurs about a point, the transformation is called a dilation and the "point" is called the dilation centre.

Hereof, how do you stretch and compress 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 ).

What are the 4 types of transformations?

There are four main types of transformations: translation, rotation, reflection and dilation.

34 Related Question Answers Found

How do you vertically stretch a graph?

Key Points
  1. When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
  2. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ) .
  3. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .

How do you know if you have vertical compression?

When you multiply a function by a positive a you will be performing either a vertical compression or vertical stretching of the graph. If 0 < a < 1 you have a vertical compression and if a > 1 then you have a vertical stretching.

How do you do vertical compression?

Parent functions can be vertically stretched or compressed by multiplying the function by some value 'a'. If a is larger than 1, then the function is vertically stretched by a factor of a. If a is between 0 and 1, then the function is vertically compressed by a factor of a.

How do you find Asymptotes?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.
  1. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
  2. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.

How do you stretch vertically by a factor of 2?


Combining Operations
  1. Stretch f vertically by a factor of 2, and then shift f up 3 units: 2f (x) + 3 = 2(2x2) + 3 = 4x2 + 3.
  2. Shrink f horizontally by a factor of 5, and then shift f right 2 units: f (5(x - 2)) = 2(5(x - 2))2 = 2(25)(x - 2)2 = 50(x - 2)2.

What is an even function?

DEFINITION. A function f is even if the graph of f is symmetric with respect to the y-axis. Algebraically, f is even if and only if f(-x) = f(x) for all x in the domain of f. A function f is odd if the graph of f is symmetric with respect to the origin.

What is transformation formula?

f (x) = x2. A function transformation takes whatever is the basic function f (x) and then "transforms" it (or "translates" it), which is a fancy way of saying that you change the formula a bit and thereby move the graph around.

How do you find the vertex?

Steps to Solve
  1. Get the equation in the form y = ax2 + bx + c.
  2. Calculate -b / 2a. This is the x-coordinate of the vertex.
  3. To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

How do you know if a graph is stretched or compressed?

A General Note: Vertical Stretches and Compressions
If a>1 , then the graph will be stretched. If 0<a<1 0 < a < 1 , then the graph will be compressed. If a<0 , then there will be combination of a vertical stretch or compression with a vertical reflection.

How do you find a vertical asymptote?


To find the vertical asymptote(s) of a rational function, simply set the denominator equal to 0 and solve for x. We mus set the denominator equal to 0 and solve: This quadratic can most easily be solved by factoring the trinomial and setting the factors equal to 0. There are vertical asymptotes at .

How do you graph compression?

In general, if y = F(x) is the original function, then you can vertically stretch or compress that function by multiplying it by some number a: If a > 1, then aF(x) is stretched vertically by a factor of a. For example, if you multiply the function by 2, then each new y-value is twice as high.

How do you stretch and compress a graph?

A General Note: Vertical Stretches and Compressions
If a > 1 displaystyle a>1 a>1, then the graph will be stretched. If 0 < a < 1, then the graph will be compressed. If a < 0 displaystyle a<0 a<0, then there will be combination of a vertical stretch or compression with a vertical reflection.

How do you stretch a function?

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 ).

How do you stretch a parabola horizontally?

The function y=x2+b has a graph which simply looks like the standard parabola with the vertex shifted b units along the y-axis. Thus the vertex is located at (0,b). If b is positive, then the parabola moves upwards and, if b is negative, it moves downwards. Similarly, we can translate the parabola horizontally.