What Is Your Own Description And Definition

What Is In Your Own Words The Description And Definition Of A Fun

1. What is, in your own words, the description and definition of a function? Include the following terms: domain, range, inverse, degree, and roots. What are two ways you use functions in everyday life? For example, how do you use functions to estimate your cell-phone bill? (150 words)

2. You have learned quadratic equations and quadratic functions. Except for the red and blue colors as I highlighted, are the quadratic equation and quadratic function different? Are they the same? Why and Why not? Please explain. (150 words)

3. See attached page. (150 words)

Paper For Above instruction

A function is a relation between a set of inputs and a set of permissible outputs where each input corresponds to exactly one output. In mathematical terms, the domain of a function is the set of all possible input values, while the range is the set of all possible output values that the function can produce. An inverse of a function is a new function that reverses the original, such that if the original function maps an input to an output, the inverse maps that output back to the input. The degree of a polynomial function indicates the highest power of the variable in the expression, determining its overall shape and complexity. Roots of a function are the points where the function intersects the x-axis, i.e., the solutions to the equation when the function equals zero. In everyday life, functions are used in various ways, such as estimating phone bills by using data plans that correlate the number of calls, texts, and data usage to the total cost. Another example is calculating body mass index (BMI), which involves a function that relates weight and height to an individual's health status.

Quadratic equations and quadratic functions are closely related but serve different conceptual purposes. A quadratic equation is an algebraic equation of the second degree, typically expressed as ax² + bx + c = 0, where a ≠ 0. Its solutions—roots—are the values of x that satisfy the equation. A quadratic function, on the other hand, is a polynomial function expressed as f(x) = ax² + bx + c, which graphs as a parabola. While the quadratic equation finds the specific x-values where the parabola intersects the x-axis, the quadratic function describes the entire curve's behavior. Both share similar algebraic structure, but one is an equation seeking roots, and the other is a function representing a relationship that can be analyzed graphically and analytically. They are intrinsically connected but serve distinct analytical purposes.

Without additional details from the attached page, the following segment summarizes the general understanding of quadratic equations and functions based on core mathematical principles, emphasizing their relationship and differences.

References

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