Answer:
To explain the concept of a vertical stretch, let's start by understanding what it means in mathematics. In mathematical functions, a vertical stretch refers to a transformation that changes the scale of the graph vertically without affecting its shape or position horizontally. This transformation is achieved by multiplying the function by a constant value greater than 1.
To illustrate this concept step by step, let's consider a simple linear function: f(x) = x. We will apply a vertical stretch to this function.
Step 1: Start with the original function f(x) = x.
Step 2: Choose a constant value greater than 1 to represent the amount of vertical stretch. Let's say we choose a value of 2.
Step 3: Multiply the original function by the chosen constant value. In this case, we multiply f(x) = x by 2:
g(x) = 2 * f(x)
= 2 * x
Step 4: Simplify the equation if necessary. In this case, there is no further simplification needed.
The resulting function g(x) = 2x represents the vertically stretched version of the original function f(x) = x. The graph of g(x) will be twice as tall as the graph of f(x), but it will maintain the same shape and position horizontally.
Now, let's move on to the top five credible references used to explain this concept. Please note that as an AI language model, I don't have direct access to external sources such as print encyclopedias or academic journals. However, I can provide you with an example list of references that you can use to explore further:
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