How do you calculate horizontal compression?

How do you calculate horizontal compression?

Given a function f(x) , a new function g(x)=f(bx) g ( x ) = f ( b x ) , where b is a constant, is a horizontal stretch or horizontal compression of the function f(x) . If b>1 , then the graph will be compressed by 1b .

What does horizontally compressed mean?

Horizontal compressions occur when the function’s base graph is shrunk along the x-axis and, consequent, away from the y-axis.

How do you write compressed horizontally?

If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x) y = f ( x ) , the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression. Consider the function y=x2 y = x 2 .

What does compressed by a factor of 1/2 mean?

So by definition, k should be called the horizontal compression factor of the function, meaning if k=12, the graph is horizontally compressed by a factor of 12, and since stretching is the inverse of compressing you could also say the graph is horizontally stretched by a factor of 2.

How do you do a horizontal stretch by a factor of 1 2?

When we horizontally stretch g(x) by a scale factor of 1/2, we obtain h(x). Let’s start with g(x). We can horizontally stretch f(x) to obtain g(x), so we divide the input value of f(x) by 5 to obtain g(x)’s expression: f(x/5). This means that in terms of f(x), g(x) = f(x/5) and h(x)= f(x/10).

How do you stretch a horizontal 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.

What is a vertical compression by a factor of 2?

The graph of g(x)=12×2 g ( x ) = 1 2 x 2 is compressed vertically by a factor of 2; each point is half as far from the x -axis as its counterpart on the graph of y=x2.

How do you compress a factor?

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.

What is vertical and horizontal compression?

For horizontal graphs, the degree of compression/stretch goes as 1/c, where c is the scaling constant. Vertically compressed graphs take the same x-values as the original function and map them to smaller y-values, and vertically stretched graphs map those x-values to larger y-values.

How do you vertically compress by a factor of 1 2?

In general, when a function is compressed vertically by a (where 0 < a < 1), the graph shrinks by the same scale factor. Let’s apply the concept to compress f(x) = 6|x| + 8 by a scale factor of 1/2. To compress f(x), we’ll multiply the output value by 1/2.

How do you convert a function to a horizontally compressed function?

This occurs when the x-value of a function is multiplied by a constant c whose value is greater than 1. That is, to use the expression listed above, the equation which takes a function f (x) and transforms it into the horizontally compressed function g (x), is given by

What does a horizontally compressed graph mean?

A horizontally compressed graph means that the transformed function requires smaller values of x than the original function in order to produce the same y-values. If a function has been horizontally stretched, larger values of x are required to map to the same y-values found in the original function.

What is the difference between horizontal compression and vertical compression?

It is also important to note that, unlike horizontal compression, if a function is vertically transformed by a constant c where 0<1″, then that function is said to be compressed by a factor of c (recall for horizontal compression that factor is 1/c ).

What is a constant in horizontal transformation?

For horizontal transformations, a constant must act directly on the x-variable, as opposed to acting on the function as a whole. There are three kinds of horizontal transformations: translations, compressions, and stretches.