H(x)=k * f(x) represents:
The equation H(x) = k * f(x) represents the composition of a constant k with a function f(x)
The equation H(x) = k * f(x) represents the composition of a constant k with a function f(x).
In this equation, f(x) represents a mathematical function that takes in a value of x and produces an output. This could be any type of function such as a polynomial, trigonometric, exponential, or logarithmic function.
The constant k is multiplied by the output of f(x) to create the function H(x). The purpose of this constant is to scale or stretch the graph of f(x) vertically. If k is positive, it will stretch the graph vertically by a factor of k. If k is negative, it will reflect the graph vertically and also stretch it by a factor of |k|.
For example, let’s say f(x) = x^2, representing a quadratic function. If k = 3, then H(x) = 3 * f(x) = 3 * x^2. This means that every y-value of the original function f(x) is multiplied by 3, resulting in a vertically stretched graph of H(x).
Similarly, if k = -2, then H(x) = -2 * f(x) = -2 * x^2. In this case, the graph of f(x) will be reflected vertically and stretched by a factor of 2.
In summary, the equation H(x) = k * f(x) represents the composition of a constant with a function, resulting in a new function that is a scaled or stretched version of the original function.
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