Contents
How do you find the horizontal stretch of a function?
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 horizontal stretch in an equation?
horizontal stretching/shrinking changes the x -values of points; transformations that affect the x -values are counter-intuitive. Vertical/Horizontal Stretching/Shrinking usually changes the shape of a graph. (more mathematical cats)
What is a horizontal stretch by 4?
stretch by a factor of 4, horizontal stretch by a factor of 2, reflection in the y-axis, translation 3 units up and 2 units right. Plugging these values into the general form f(x) = a f[ b(x − h)] + k where f(x) = , we get f(x) = 4[ ] + 3. This can be simplified to f(x) = + 3.
What is an example of a horizontal stretch?
When we multiply a function’s input by a positive constant, we get a function whose graph is stretched or compressed horizontally in relation to the graph of the original function. The graph of y=(0.5x)2 y = ( 0.5 x ) 2 is a horizontal stretch of the graph of the function y=x2 y = x 2 by a factor of 2.
How do you know if it is a horizontal stretch or 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.
How do you show a horizontal shrink?
A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis. if k > 1, the graph of y = f (k•x) is the graph of f (x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.
What is an example of a horizontal compression?
The graph of y=(0.5x)2 y = ( 0.5 x ) 2 is a horizontal stretch of the graph of the function y=x2 y = x 2 by a factor of 2. The graph of y=(2x)2 y = ( 2 x ) 2 is a horizontal compression of the graph of the function y=x2 y = x 2 by a factor of 2.
What is the definition of a horizontal stretch?
This is called a horizontal stretch. A point (a,b) (a, b) on the graph of y= f(x) y = f (x) moves to a point (ka,b) (k a, b) on the graph of y =f(x k) y = f (x k). This transformation type is formally called horizontal scaling (stretching/shrinking).
What is a horizontal stretch and shrink in math?
Similarly, what is a horizontal shrink in math? 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 the difference between vertical stretch and horizontal compression?
How to calculate horizontal and vertical graph stretches?
Horizontal And Vertical Graph Stretches and Compressions. (Part 1) The general formula is given as well as a few concrete examples. y = c f(x), vertical stretch, factor of c
Is it possible to stretch a function horizontally?
Before we start stretching functions horizontally by a certain factor, remember these pointers to stretch graphs faster horizontally: Only stretch the base of the graph horizontally so that the y-coordinates would remain in the same position. Since the y-coordinates will remain the same, the y-intercept stays the same as well.