Question: How Can You Tell If A Stretch Is Horizontal Or Vertical?

What does a horizontal stretch look like?

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)..

How do you do a horizontal 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.

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.

How do you compress a horizontal function?

To shrink or compress horizontally by a factor of c, replace y = f(x) with y = f(cx). Note that if |c|<1, that's the same as scaling, or stretching, by a factor of 1/c.

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 does a vertical shrink look like?

The y -values are being multiplied by a number between 0 and 1 , so they move closer to the x -axis. This tends to make the graph flatter, and is called a vertical shrink. In both cases, a point (a,b) on the graph of y=f(x) y = f ( x ) moves to a point (a,kb) ( a , k b ) on the graph of y=kf(x) y = k f ( x ) .

How do you find a horizontal asymptote?

To find horizontal asymptotes:If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.More items…•

What is the horizontal asymptote of a function?

A horizontal asymptote for a function is a horizontal line that the graph of the function approaches as x approaches ∞ (infinity) or -∞ (minus infinity).

How do you know if compression is vertical or 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.

How do you do vertical compression?

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.

What does stretched by a factor of 2 mean?

Some texts always use a factor greater than 1; they say that f(2x) is compressed by a factor of 2 (meaning x is divided by 2) f(x/2) is stretched by a factor of 2 (meaning x is multiplied by 2) In general, f(cx) is stretched by a factor of 1/c if 0 < c < 1, and compressed by a factor of c if c > 1.

What is a 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 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.

What are the 3 different cases for finding the horizontal asymptote?

There are 3 cases to consider when determining horizontal asymptotes:1) Case 1: if: degree of numerator < degree of denominator. then: horizontal asymptote: y = 0 (x-axis) ... 2) Case 2: if: degree of numerator = degree of denominator. ... 3) Case 3: if: degree of numerator > degree of denominator.