What does it mean when a function is stretched horizontally?
What does it mean when a function is stretched horizontally?
Horizontal stretching means that you need a greater x-value to get any given y-value as an output of the function. You can see this on the graph. See how the maximum y-value is the same for all the functions, but for the stretched function, the corresponding x-value is bigger.
What is the rule for a 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. Consider the function y=x2 y = x 2 .
How do you horizontally stretch a graph by 2?
To stretch or shrink the graph in the y direction, multiply or divide the output by a constant. 2f (x) is stretched in the y direction by a factor of 2, and f (x) is shrunk in the y direction by a factor of 2 (or stretched by a factor of ). Here are the graphs of y = f (x), y = 2f (x), and y = x.
How do you compress horizontally?
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 shift a function horizontally?
A General Note: Horizontal Shift Given a function f, a new function g ( x ) = f ( x − h ) \displaystyle g\left(x\right)=f\left(x-h\right) g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.
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.
How do you shrink a graph horizontally?
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 does it mean to shrink a graph horizontally?
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).
Is 1 2x a horizontal stretch?
Horizontal Stretch The graph of f(12x) f ( 1 2 x ) is stretched horizontally by a factor of 2 compared to the graph of f(x). Further, if (x,y) is a point on the graph of f(x), then (2x,y) ( 2 x , y ) is a point on the graph of f(12x).
How do you shift a quadratic equation horizontally?
You can represent a horizontal (left, right) shift of the graph of f(x)=x2 f ( x ) = x 2 by adding or subtracting a constant, h , to the variable x , before squaring. If h>0 , the graph shifts toward the right and if h<0 , the graph shifts to the left.
How do you tell if a stretch is horizontal or vertical?
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 ) .
How do you stretch a graph?
To stretch or shrink the graph in the x direction, divide or multiply the input by a constant. As in translating, when we change the input, the function changes to compensate. Thus, dividing the input by a constant stretches the function in the x direction, and multiplying the input by a constant shrinks the function in the x direction.
How do you calculate 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. Horizontal shifts can be applied to all trigonometric functions.
What is a horizontal stretch of a function?
A horizontal stretching is the stretching of the graph away from the y-axis. When a function is horizontally stretched by a factor, k, the x-value of the function is multiplied by the factor k.