stretch is a transformation that results in the distance from the x-axis every point growing by a scale factor greater than 1 and a vertical compression is a transformation that results in the distance from the x-axis of every point shrinking by a scale factor between 0 and 1.

Is vertical compression shrink or stretch?

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k.

What is a vertical stretch example?

Examples of Vertical Stretches and Shrinks

(2) g(x) = sin (x). 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.

What does a vertical compression affect?

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.

What is vertical compression?

Vertical compression means making the y-value smaller for any given value of x, and you can do it by multiplying the entire function by something less than 1. Horizontal stretching means making the x-value bigger for any given value of y, and you can do it by multiplying x by a fraction before any other operations.

What does vertical stretch mean?

What is a vertical stretch? 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 an equation is stretched or compressed?

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 impact do vertical stretches and compressions have on the rate of change?

So what we can say that in vertical compression, in vertical stretch stretch, mint, the the rate of change will be increased and in political compression the rate of change will be decreased.

What is a horizontal stretch and compression?

If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function.

What is a compression in math?

A compression occurs when a mathematical object is scaled by a scale factor less in absolute value than one. When a compression occurs, the image is smaller than the original mathematical object. If the scaling occurs about a point, the transformation is called a dilation and the “point” is called the dilation centre.

When you perform a horizontal stretch or compression What happens to the vertical intercept?

In a horizontal compression, the y-intercept is unchanged. Example: Starting with f1(x) = 1 x , we can obtain f2(x) = f1(2x) = 1 2x . The graph of 1 2x is the graph of 1 x compressed by a factor of 2 horizontally.

What is horizontal and vertical stretch?

vertical stretching/shrinking changes the y -values of points; transformations that affect the y -values are intuitive. horizontal stretching/shrinking changes the x -values of points; transformations that affect the x -values are counter-intuitive.

What is the difference between vertical and horizontal?

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.

How do you know if a graph is stretched or compressed?

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 is a vertical stretch equation?

y=f(x) y=2f(x) vertical stretch; y -values are doubled; points get farther away.

What is a vertical stretch by a factor of 2?

Stretching f(x) vertically by a factor of 2 will result in h(x) being equal to 2 times f(x). Stretching f(x) vertically by a factor of 3 will result to h(x) being equal to 3 times f(x). Hence, h(x) = 3|x|.