How do you factor 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.
What is a horizontal shrink by 1 2?
The horizontal shrink means you shrink x by a factor of 1/2. Currently the slope on the right side of the V is 1, so to “shrink” it, you actually DIVIDE by 1/2, giving you a new slope of 2.
What is the horizontal stretch by a factor of 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 a horizontal stretch in math?
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. • 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 a horizontal stretch by a factor of 3?
If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.
What is a vertical compression by a factor of 1 3?
Say if you have an absolute value function f(x)= |4-x|, the way you would vertically compress it is by affecting it’s slope. If you multiply the number in front of x by 1 1/3 or 1.3333 repeating. The 1 aspect of 1 and 1/3 helps the slope stay constant, the 1/3 or . 3333 repeating compresses it vertically by 1/3.
What is vertical stretch?
Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. The input values will remain the same, so the graph’s coordinate points will now be (x, ay). This means that if f(x) = 5x + 1 is vertically stretched by a factor of 5, the new function will be equivalent to 5 · f(x).
How do you write a horizontal stretch by a factor of 2?
Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 3, and the equation of a function stretched horizontally by a factor of 2 and then shifted 3 units right is y = f ( (x – 3)) = f ( x – ).
How do you stretch vertically by a factor of 3?
If g(x) = 3f (x): For any given input, the output iof g is three times the output of f, so the graph is stretched vertically by a factor of 3. If g(x) = f (3x): For any given output, the input of g is one-third the input of f, so the graph is shrunk horizontally by a factor of 3.
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 vertical stretch or shrink?
A vertical stretching is the stretching of the graph away from the x-axis. 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 causes horizontal compression?
Tension and shear cause horizontal movement. Compression causes upward vertical movement. Shear causes horizontal movement. Tension causes downward vertical movement. At a reverse fault plane, c ompression causes upward vertical movement.
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.