How do you determine vertical and horizontal 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.
Which exponential function shows a vertical stretch?
Exponential Functions
| Figure 1 | Figure 2 |
|---|---|
| Vertical Stretch , that has been stretched vertically with respect to the base function, | Vertical Shrink , that has been compressed vertically with respect to the base function, f2 (x) = 2 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 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 does horizontal stretch work?
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 horizontal stretch of an exponential function?
While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function f(x)=bx f ( x ) = b x by a constant |a|>0 .
What is a horizontal stretch?
What is a vertical stretch?
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.
How do you find the vertical and horizontal asymptote of an exponential function?
Certain functions, such as exponential functions, always have a horizontal asymptote. A function of the form f(x) = a (bx) + c always has a horizontal asymptote at y = c. For example, the horizontal asymptote of y = 30e–6x – 4 is: y = -4, and the horizontal asymptote of y = 5 (2x) is y = 0.
What is a vertical compression?
Vertical compression means making the y-value smaller for any given value of x, and you can do it by multiplying the entire function by something less than 1. Horizontal stretching means making the x-value bigger for any given value of y, and you can do it by multiplying x by a fraction before any other operations.
Whats a horizontal stretch?
Horizontal stretches are among the most applied transformation techniques when graphing functions, so it’s best to understand its definition. Horizontal stretches happen when a base graph is widened along the x-axis and away from the y-axis. Understanding the common parent functions we might encounter.
