Create a table for the function [latex]g\left(x\right)=\frac{3}{4}f\left(x\right)[/latex].The graph is a transformation of the toolkit function [latex]f\left(x\right)={x}^{3}[/latex].

Replace every $\,x\,$ by $\,\frac{x}{k}\,$ to

What is the new equation?

and multiplying the $\,y$-values by $\,\frac13\,$. A General Note: Horizontal Stretches and Compressions.

Horizontal And Vertical Graph Stretches and Compressions. To properly determine fabric stretch, you must gently stretch the fabric and observe the recovery, similar to the performance needed as if it were made into a garment, going to be going over your head to put on, or fitting on your body. • To write the mapping rule of the function, notice what happens to the numerical coefficient of x: With the basic cubic function at the same input, [latex]f\left(2\right)={2}^{3}=8[/latex]. What is the new equation? 3. a = 1.

This moves the points closer to the $\,x$-axis, which tends to make the graph flatter. The stretch in the pipe is found with reference to some fixed point which will not move when extra pull is applied (SI UNITS) Multiply the previous $\,y\,$-values by $\,k\,$, giving the new equation vertical shrink; Here is the thought process you should use when you are given the graph of $\,y=f(x)\,$ Points on the graph of This equals the length of pipe between the stuck point and surface. Master the ideas from this section Replacing x with x n results in a horizontal stretch by a factor of n .. where p is the horizontal stretch factor, (h, k) is the coordinates of the vertex. You wouldn’t want fabric to be stretched beyond its capacity when wearing it, so likewise, yanking on the fabric will not give you the best percentage estimate, and it will likely warp the fabric, compromising its quality. The horizontal stretch affects the graph by stretching (or compressing) the graph horizontally. For the next two transformations, why don’t you try graphing them on your own.

Each change has a specific effect that can be seen graphically.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. [latex]\begin{cases}\left(0,\text{ }1\right)\to \left(0,\text{ }2\right)\hfill \\ \left(3,\text{ }3\right)\to \left(3,\text{ }6\right)\hfill \\ \left(6,\text{ }2\right)\to \left(6,\text{ }4\right)\hfill \\ \left(7,\text{ }0\right)\to \left(7,\text{ }0\right)\hfill \end{cases}[/latex]This means that for any input [latex]t[/latex], the value of the function [latex]Q[/latex] is twice the value of the function [latex]P[/latex]. Then[latex]g\left(4\right)=\frac{1}{2}\cdot{f}(4) =\frac{1}{2}\cdot\left(3\right)=\frac{3}{2}[/latex]We do the same for the other values to produce this table.The result is that the function [latex]g\left(x\right)[/latex] has been compressed vertically by [latex]\frac{1}{2}[/latex].

C > 1 compresses it; 0 < C < 1 stretches it This equals the length of pipe between the stuck point and surface. We’ve narrowed down stretch characteristics in common groups to make online fabric shopping even easier:

Conic Sections: Hyperbola example Directional stretch and stretch percentage are important features when choosing the right fabric for your project. y2= 2, then there is a horizontal stretch of 2.

Here is the thought process you should use when you are given the graph of Over the years there has been some debate regarding the surface pull required to achieve this condition.

The key concepts are repeated here. vertical stretching/shrinking changes the $y$-values of points;

The input values, [latex]t[/latex], stay the same while the output values are twice as large as before.A function [latex]f[/latex] is given in the table below. Do a vertical shrink, where $\,(a,b) \mapsto (a,\frac{b}{4})\,$.