When it comes to understanding the behavior of functions, it is important to know how different transformations affect their graphs. One of the most common transformations is a vertical shrink, which is a change in the vertical scale of a function.
A vertical shrink occurs when we multiply the output values of a function by a constant factor that is less than one. This causes the graph of the function to compress vertically, making it appear narrower and taller than the original graph.
To understand how this works, consider the equation of a simple function f(x) = x. If we multiply this function by a constant factor of 0.5, we get a new function g(x) = 0.5x. The graph of this new function is a vertical shrink of the original graph.
To see this, let’s compare the graphs of f(x) and g(x) side by side. On the graph of f(x), the point (1,1) is located at a height of 1 unit above the x-axis. However, on the graph of g(x), the corresponding point (1,0.5) is located only 0.5 units above the x-axis. This means that the entire graph of g(x) is compressed vertically by a factor of 0.5, making it half as tall as the original graph of f(x).
This concept can be applied to any function, not just linear ones. For example, consider the function h(x) = x^2. If we multiply this function by a constant factor of 0.25, we get a new function k(x) = 0.25x^2. The graph of k(x) is a vertical shrink of the original graph of h(x).
To visualize this, we can agin compare the graphs of h(x) and k(x) side by side. On the graph of h(x), the point (1,1) is located 1 unit above the x-axis and 1 unit to the right of the y-axis. However, on the graph of k(x), the corresponding point (1,0.25) is located only 0.25 units above the x-axis and 1 unit to the right of the y-axis. This means that the entire graph of k(x) is compressed vertically by a factor of 0.25, making it much narrower and taller than the original graph of h(x).
A vertical shrink is a transformation that compresses the graph of a function vertically by multiplying its output values by a constant factor that is less than one. This makes the graph appear narrower and taller than the original graph, and can be applied to any function. Understanding this concept is essential for analyzing the behavior of functions and making accurate predictions about their graphs.
How Do You Know If Its Vertical Shrink Or Stretch?
To determine whether a function has undergone a vertical stretch or compression, we need to look at the constant by which it has been multiplied. If the constant is greater than 1, the function has undergone a vertical stretch, which means that the function has been elongated vertically, making it appear taller than the original function. On the other hand, if the constant is betwen 0 and 1, the function has undergone a vertical compression, which means that the function has been shortened vertically, making it appear shorter than the original function.
To make it simpler, here’s a summary:
– If the constant is greater than 1, it’s a vertical stretch.
– If the constant is between 0 and 1, it’s a vertical compression.
Remember, this applies to functions that have been multiplied by a positive constant.
What Is A Vertical Shrink Example?
A vertical shrink is a transformation of a function that results in a compressed or contracted graph in the y-direction. This means that the distance between the points on the graph and the x-axis is reduced by a certain factor. An example of a vertical shrink can be seen in the function f(x) = 2x, whre the graph of the function is compressed vertically by a factor of 1/2. Another example is the function g(x) = -3x, where the graph is compressed vertically by a factor of 1/3. In general, a vertical shrink by a factor of k means that the y-coordinate of each point on the graph is multiplied by k. This results in a graph that is narrower and closer to the x-axis than the original function.
What Is Vertical Stretch Shrink?
Vertical stretch and shrink are transformations that alter the overall dimensions of a base graph without changing its shape. A vertical stretch occurs when a graph is elongated vertically, wile a vertical shrink occurs when a graph is compressed vertically. These transformations are applied by multiplying the y-coordinates of the base graph by a factor greater than 1 for stretches or less than 1 for shrinks. The effect of the transformation is to make the graph taller or shorter, but not wider or narrower. Vertical stretches and shrinks are a type of dilation, which is a transformation that changes the size of a figure while keeping its shape. a vertical stretch or shrink changes the height of a graph while maintaining its shape.
How Do You Tell If An Equation Is A Vertical Shrink?
To determine whether an equation represents a vertical shrink, we need to analyze the value of the scaling factor ‘a’ in the equation. A vertical shrink occurs when the value of ‘a’ is betwen 0 and 1, which means that the parent function is compressed vertically.
Here are the steps to follow to determine if an equation is a vertical shrink:
1. Identify the parent function f(x) in the equation.
2. Determine the value of ‘a’ in the equation.
3. If ‘a’ is between 0 and 1, the equation represents a vertical shrink of the parent function.
4. If ‘a’ is greater than 1, the equation represents a vertical stretch of the parent function.
5. If ‘a’ is equal to 1, the equation represents the parent function without any vertical compression or stretching.
It is important to note that a vertical shrink does not change the shape of the parent function, but only reduces its height. The resulting function will be narrower and closer to the x-axis than the parent function.
Conclusion
A vertical shrink is a transformation that compresses the graph of a function vertically, making it narrower than the original graph. It is achieved by multiplying the function by a positive constant between 0 and 1. The resulting function has the same shape as the original function, but its y-values are decreased by a factor of the constant. This transformation can be useful in various applications, such as when dealing with data sets that have a wide range of values and need to be scaled down to fit within a certain range. Understanding how to perform a vertical shrink is an important skill for anyne working with functions and their graphs. By knowing how to apply this transformation, we can manipulate functions to better suit our needs and gain a deeper understanding of their behavior.
