How do you know if its a vertical or horizontal stretch?
How do you know if its a vertical or horizontal stretch?
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 ) .
- In general, a horizontal stretch is given by the equation y=f(cx) y = f ( c x ) .
What is a vertical and horizontal 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 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.
What is horizontal shrink?
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.
How do you find vertical dilation?
Vertical dilation. If y is replaced by y/B in a formula and B>0, then the effect on the graph is to dilate it by a factor of B in the vertical direction.
Is a vertical stretch similar?
A vertical compression is the same as a vertical stretch, but where the scaling factor is between 0 and 1. Vertical stretches preserve the horizontal distance. In quarter 1, this meant that a figure that had been stretched vertically had the same width as the original figure.
What is the difference between a vertical stretch and a 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 a vertical compression look like on a graph?
What’s the difference between shift and translation?
Shifts. A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.
What is horizontal translation?
What is a Horizontal Translation? Horizontally translating a graph is equivalent to shifting the base graph left or right in the direction of the x-axis. A graph is translated k units horizontally by moving each point on the graph k units horizontally. Definition.
How do you find the horizontal shift?
The horizontal shift is C. The easiest way to determine horizontal shift is to determine by how many units the “starting point” (0,0) of a standard sine curve, y = sin(x), has moved to the right or left.
How do you do a horizontal shrink?
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.
How do you scale a graph horizontally?
Horizontal scaling means the stretching or shrinking the graph of the function along the x-axis. Horizontal scaling can be done by multiplying the input with a constant. The graph stretches if the value of C < 1, and the graph will shink if the value of C > 1.
How do you find the vertical and horizontal scale?
To determine the amount of vertical exaggeration used to construct a profile, simply divide the real-world units on the horizontal axis by the real-world units on the vertical axis. If the vertical scale is one 1″=1000′ and the horizontal scale is 1″=2000′, the vertical exaggeration is 2x (2000’/1000′).
What is the horizontal scale?
In horizontal scaling (a.k.a. “scaling out”), you get the additional resources into your system by adding more machines to your network, sharing the processing and memory workload across multiple devices.
What is a vertical scale for a graph?
Vertical scaling refers to changing the shape and size of the graph of the function along the y-axis and is done by multiplying the function by some constant.