# What is a vertical stretch on a graph?

Table of Contents

## What is a vertical stretch on a graph?

Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. This results in the graph being pulled outward but retaining the input values (or x). When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis.

## How do you tell if a graph is vertically 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.

## Is a horizontal stretch the same as a vertical compression?

With a parabola whose vertex is at the origin, a horizontal stretch and a vertical compression look the same.

## What does a vertical shrink look like?

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. Take a look at the graphs of f (x) and y1(x). Notice that the x-intercepts have not moved.

## How do you know if its a vertical stretch or shrink?

Key Takeaways

- When 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 a vertical stretch by a factor of 2?

Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 3, and the equation of a function stretched horizontally by a factor of 2 and then shifted 3 units right is y = f ( (x – 3)) = f ( x – ).

## 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.

## Is a vertical stretch positive or negative?

If 0 < a < 1 you have a vertical compression and if a > 1 then you have a vertical stretching. When a is negative, then this vertical compression or vertical stretching of the graph is followed by a reflection across the x-axis.

## What is a vertical compression example?

Vertical compressions occur when a function is multiplied by a rational scale factor. The base of the function’s graph remains the same when a graph is compressed vertically. 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.

## What is a vertical compression by a factor of 2 3?

(1) A vertical compression of 2/3 is achieved by multiplying the function by 2/3. This reduces the amplitude by a factor of 2/3. Thus the leading coefficient is 2/3. (2) A reflection in the x-axis is achieved by multiplying f(x) by -1.

## What is a vertical compression by a factor of 1 3?

When you compress it vertically, it is the same as stretching it horizontally. When you stretch a function horizontally, the f(x) values get smaller and smaller. So to make f(x) smaller, multiply the function by (1/3).

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

Stretch and Shrink A function’s graph is vertically stretched or shrunk by multiplying the function rule by some constant a>0: g(x)=a⋅f(x). All vertical distances from the graph to the x-axis are changed by the factor a. Thus, preserving any x-intercepts.

## How do you find the vertical and horizontal asymptotes?

The vertical asymptotes will occur at those values of x for which the denominator is equal to zero: x2 − 4=0 x2 = 4 x = ±2 Thus, the graph will have vertical asymptotes at x = 2 and x = −2. To find the horizontal asymptote, we note that the degree of the numerator is one and the degree of the denominator is two.

## How do you find a vertical asymptote?

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value). Find the asymptotes for the function . The graph has a vertical asymptote with the equation x = 1.

## How do you determine the domain and range of a rational function?

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. A rational function is a function of the form f(x)=p(x)q(x) , where p(x) and q(x) are polynomials and q(x)≠0 .

## How do you transform a rational function?

Any graph of a rational function can be obtained from the reciprocal function f(x)=1x f ( x ) = 1 x by a combination of transformations including a translation, stretches and compressions.

## What is a rational parent function?

The parent function of a rational function is f(x)=1x and the graph is a hyperbola . The domain and range is the set of all real numbers except 0 . Domain:{x | x≠0}Range:{y | y≠0} Excluded value. In a rational function, an excluded value is any x -value that makes the function value y undefined.

## How do you solve a rational function by graphing?

Process for Graphing a Rational Function

- Find the intercepts, if there are any.
- Find the vertical asymptotes by setting the denominator equal to zero and solving.
- Find the horizontal asymptote, if it exists, using the fact above.
- The vertical asymptotes will divide the number line into regions.
- Sketch the graph.

## Is a reciprocal function continuous?

Is a reciprocal function continuous? A function is not continuous at any point not in its domain. Hence your reciprocal function is continuous at every value of x other than x=0, where it is discontinuous.

## What is the reciprocal of a function?

The reciprocal function of a function f(x) is 1/f(x). The general form of a reciprocal function is r(x) = a / (x – h) + k. The vertical asymptote of r(x) is x = h. The horizontal asymptote of r(x) is y = k.