What is a vertical compression 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 calculate vertical compression?

Given a function f(x) , a new function g(x)=af(x) g ( x ) = a f ( x ) , where a is a constant, is a vertical stretch or vertical compression of the function f(x) . If a>1 , then the graph will be stretched. If 0

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.

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 stretch vertically 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 – ). Example: f (x) = 2×2.

Is vertical stretch and horizontal compression the same?

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

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.

Is a vertical stretch negative or positive?

When you multiply a function by a positive a you will be performing either a vertical compression or vertical stretching of the graph. If 0 < a < 1 you have a vertical compression and if a > 1 then you have a vertical stretching.

How do you know how much a graph is compressed?

Identify the value of a. Multiply all range values by a. If a > 1 \displaystyle a>1 a>1, the graph is stretched by a factor of a. If 0 < a < 1 \displaystyle { 0 }<{ a }<{ 1 } 0

How do you stretch vertically?

Key Points 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 ) .

Is I horizontal or vertical?

Anything parallel to the horizon is called horizontal. As vertical is the opposite of horizontal, anything that makes a 90-degree angle (right angle) with the horizontal or the horizon is called vertical. So, the horizontal line is one that runs across from left to right….What is Horizontal?

When does a function have a vertical compression?

What is a vertical compression? 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. Only the output values will be affected.

Which is the result of f ( x ) being vertically compressed?

The function g (x) is the result of f (x) being vertically compressed by a factor of 1/2. The function h (x) is the result of g (x) being vertically compressed by a factor of 1/3. As suggested, let’s go ahead and find the x and y-intercepts of f (x).

How to write a formula for a compression?

How To: Given a description of a function, sketch a horizontal compression or stretch. 1 Write a formula to represent the function. 2 Set g(x) = f (bx) g ( x) = f ( b x) where b> 1 b > 1 for a compression or 0 for a stretch. More

What happens to a graph when it is compressed vertically?

As we may have expected, when f (x) is compressed vertically by a factor of 1/2 and 1/4, the graph is also compressed by the same scale factor. 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.