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Chapter 2: Problem 98

You will be developing functions that model given conditions. Describe one advantage of using \(f(x)\) rather than \(y\) in a function's equation.

Short Answer

Expert verified
The main advantage of using \(f(x)\) notation over \(y\) is that it concisely conveys that \(y\) is a function of \(x\), meaning \(y\) depends on the value of \(x\).

Step by step solution

01

Understanding of function notation

In mathematics, functions are commonly represented as \(f(x)\) rather than \(y\). This is referred to as function notation. In this case, \(f\) represents the function, and \(x\) represents the input into the function. When given a particular \(x\), the function \(f\) produces an output.
02

Understanding of traditional y notation

Contrastingly, in a traditional equation such as \(y = x + 2\), \(y\) represents the output or dependent variable while \(x\) represents the input or independent variable. The equation shows the relation between \(x\) and \(y\).
03

Comparing function notation with traditional y notation

While both notations can describe the relationship between variables, there are some significant differences. One advantage of function notation is that it explicitly shows the dependent relationship of \(y\) on \(x\), i.e., the output depends on the input given. Thus \(f(x)\) can be seen as a machine that takes an input \(x\) and produces an output.

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Most popular questions from this chapter

Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=(x-1)^{2} $$

Describe one advantage of using \(f(x)\) rather than \(y\) in a function's equation. How is the domain of a function determined?

A formula in the form \(y=m x+b\) models the cost, \(y,\) of a four-year college \(x\) years after \(2003 .\) Would you expect \(m\) to be positive, negative, or zero? Explain your answer.

What must be done to a function's equation so that its graph is reflected about the \(x\) -axis?

a. Use a graphing utility to graph \(f(x)=x^{2}+1\) b. Graph \(f(x)=x^{2}+1,\) and \(g(x)=f\left(\frac{1}{2} x\right),\) and \(h(x)=f\left(\frac{1}{4} x\right)\) in the same viewing rectangle. c. Describe the relationship among the graphs of \(f, g,\) and \(h,\) with emphasis on different values of \(x\) for points on all three graphs that give the same \(y\) -coordinate. d. Generalize by describing the relationship between the graph of \(f\) and the graph of \(g,\) where \(g(x)=f(c x)\) for \(0
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