Problem 14 Evaluate. \(f(x)=-12 ;\) find ... [FREE SOLUTION]

Chapter 2: Problem 14

Evaluate. \(f(x)=-12 ;\) find \(f(-12), f(0)\), and \(f(a)\).

Short Answer

Expert verified

For all values evaluated, \(-12\), \(0\), and \(a\), the result is always \(f(x) = -12\).

Step by step solution

Understand the Function

The function given is constant, defined as \( f(x) = -12 \). This means that \( f(x) \) always equals \(-12\), regardless of the value of \(x\).

Evaluate \( f(-12) \)

Since \( f(x) = -12 \) for any \(x\), substituting \( x = -12 \) into the function, we have \( f(-12) = -12 \).

Evaluate \( f(0) \)

For the value \( x = 0 \), substitute into the function \( f(x) = -12 \) to find \( f(0) = -12 \).

Evaluate \( f(a) \)

Because the function is constant for any \(x\), substituting \( x = a \) still results in \( f(a) = -12 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Evaluate Function

To evaluate a function simply means to find its value for specific inputs. In the context of a constant function like the one given by \(f(x) = -12\), evaluating is straightforward because regardless of the value of \(x\), the output is always \(-12\). This is a defining characteristic of a constant function.
When asked to evaluate \( f(-12) \), \( f(0) \), and \( f(a) \), you are simply applying this rule:

For \( x = -12\), since the function is constant, \( f(-12) = -12\).
For \( x = 0\), again, because the function doesn't change, \( f(0) = -12\).
For \( x = a\), the result remains unchanged, \( f(a) = -12\).

Evaluating a constant function is simple and involves recognizing the unchanging nature of its output.

Function Notation

In mathematics, function notation provides a way to express the idea of a rule that relates inputs to outputs clearly and concisely. When you see something like \( f(x) = -12 \), it's letting you know that \( f \) is a function of \( x \), and this particular function outputs \(-12\) for any input.Function notation helps streamline complex expressions:

It clearly identifies the function and its variable, eliminating ambiguity.
It simplifies the communication of mathematical relationships.
It allows for easy substitutions of different inputs to see their effects.

Whether evaluating \( f(2) \), \( f(b) \), or any other expression, function notation makes it effortless to understand what is being asked and how to perform the necessary calculations.

Algebra Concepts

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In this exercise, we focus on the concept of a constant function, which is a basic yet fundamental element of algebra.\[\]A constant function, like \( f(x) = -12 \), is unique because:

Its output remains the same no matter what input value you use.
Graphically, it is represented by a horizontal line on the Cartesian plane.
It reinforces the concept of equal outputs for any given input, underscoring consistency.

Understanding constant functions broadens your grasp of algebra as it leads into more complex scenarios involving variable functions and their behaviors.

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91影视

Evaluate. \(f(x)=-12 ;\) find \(f(-12), f(0)\), and \(f(a)\).

Short Answer

Step by step solution

Understand the Function

Evaluate \( f(-12) \)

Evaluate \( f(0) \)

Evaluate \( f(a) \)

Key Concepts

Evaluate Function

Function Notation

Algebra Concepts

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