How Do You Do A Vertical Stretch And Compression?

Is a vertical compression the same as a horizontal stretch?

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis.

A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.

• if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k..

How do you do a vertical stretch by a factor of 2?

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 ). Here are the graphs of y = f (x), y = 2f (x), and y = x.

What is horizontal shrink?

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. Consider the following base functions, (1) f (x) = x2 – 3, (2) g(x) = cos (x).

How do I compress a vertical file?

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.

What is the vertical shift of a function?

A vertical shift is when the graph literally moves vertically, up or down. The movement is all based on what happens to the y-value of the graph. The y-axis of a coordinate plane is the vertical axis. When a function shifts vertically, the y-value changes.

How do you do horizontal shift?

the horizontal shift is obtained by determining the change being made to the x-value. The horizontal shift is C. The easiest way to determine horizontal shift is to determine by how many units the “starting point” (0,0) of a standard sine curve, y = sin(x), has moved to the right or left.

How do you find the vertical stretch of a rational function?

Given a simple rational function, f, and a new function g such that , then: Ø If , then the graph of g is a vertical stretch of the graph of f by a factor of c. Ø If , then the graph of g is a vertical compression of the graph of f by a factor of c.

Is Vertical Up or down?

Vertical describes something that rises straight up from a horizontal line or plane. … The terms vertical and horizontal often describe directions: a vertical line goes up and down, and a horizontal line goes across. You can remember which direction is vertical by the letter, “v,” which points down.

What does vertical look like?

A vertical line is one the goes straight up and down, parallel to the y-axis of the coordinate plane. All points on the line will have the same x-coordinate. … A vertical line has no slope. Or put another way, for a vertical line the slope is undefined.

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.

How do you graph a vertical stretch?

Key PointsWhen 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 ) .

What is difference between horizontal and vertical?

A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line. Horizontal lines do not cross each other. Vertical lines do not cross each other.

How do you vertically stretch a quadratic equation?

If A > 1, the function is stretched vertically. If A < 1 it is compressed vertically, and if A is negative, it still scales the graph by |A|, but it is also flipped across the x-axis. For example, f(x) = x2 has a vertex of (0, 0) and opens upward, but g(x) = -x2 opens downward – but has the same vertex.

What are the 7 parent functions?

The following figures show the graphs of parent functions: linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent.

How do you find the vertical and horizontal asymptotes?

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

How do you tell if a graph is vertically stretched or compressed?

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 reflection.

What is a vertical stretch example?

Examples of Vertical Stretches and Shrinks looks like? Using the definition of f (x), we can write y1(x) as, y1 (x) = 1/2f (x) = 1/2 ( x2 – 2) = 1/2 x2 – 1. Based on the definition of vertical shrink, the graph of y1(x) should look like the graph of f (x), vertically shrunk by a factor of 1/2.

What is horizontal and vertical shift?

Vertical shifts are outside changes that affect the output ( y- ) axis values and shift the function up or down. Horizontal shifts are inside changes that affect the input ( x- ) axis values and shift the function left or right.

How do you find vertical translation?

Vertically translating a graph is equivalent to shifting the base graph up or down in the direction of the y-axis. A graph is translated k units vertically by moving each point on the graph k units vertically. g (x) = f (x) + k; can be sketched by shifting f (x) k units vertically.