What Is Horizontal Stretching? (Best solution)

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).

What is a vertical stretch?

• 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).

What are horizontal and vertical stretches?

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 makes a function horizontal stretch?

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. Given a function y=f(x) y = f ( x ), the form y=f(bx) y = f ( b x ) results in a horizontal stretch or compression.

Is a horizontal stretch a dilation?

A dilation is an enlargement (or reduction) that is “uniformly” applied to a figure. The image of a dilation is the same shape as the original figure, but is not necessarily the same size. Both the vertical length and horizontal length of a dilated figure are increased (or decreased) by the same factor.

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What is vertical and horizontal?

In geometry, we use the words vertical and horizontal for standing and sleeping respectively. 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.

How do you do a horizontal stretch?

Key Takeaways

1. When by either f(x) or x is multiplied by a number, functions can “stretch” or “shrink” vertically or horizontally, respectively, when graphed.
2. In general, a vertical stretch is given by the equation y=bf(x) y = b f ( x ).
3. In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ).

What’s the difference between vertical and horizontal?

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.

Why are horizontal stretches opposite?

Why are horizontal translations opposite? While translating a graph horizontally, it might occur that the procedure is opposite or counter-intuitive. That means: For negative horizontal translation, we shift the graph towards the positive x-axis.

What is vertical stretch?

Also, a vertical stretch/shrink by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x). Examples of Vertical Stretches and Shrinks. Consider the following base functions, (1) f (x) = x2 – 2, (2) g(x) = sin (x).

Is a stretch or 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.

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Is vertical stretch inside or outside?

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

What is horizontal dilation?

“horizontal dilation” A horizontal stretching is the stretching of the graph away from the y-axis. A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.

Is Dilation the same as stretch?

Dilation: The process of enlargement, stretching, or expansion. The word “dilatation” means the same thing. Both come from the Latin “dilatare” meaning “to enlarge or expand.”

What is the difference between vertical and horizontal dilations?

The difference occurs because vertical dilations occur when we scale the output of a function, whereas horizontal dilations occur when we scale the input of a function.