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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 52
Chapter 3, Problem 52

Find the value of the function for the given value of x.
f(x)={3if 0<x≤410−2[[5−x]]if x>4, for , for x=6.2f(x)=\(\begin{cases}\)3 & \(\text{if }\)0<x\(\leq\)4\\ 10-2[\(\left\]\lbrack\)5-x]\(\right\[\rbrack\) & \(\text{if }\)x>4,\(\text{ for }\]\end{cases}\),\(\text{ for }\)x=6.2

Verified step by step guidance
1
First, carefully read the piecewise function definition to understand the different cases for ƒ(x). It seems the function has different values depending on the value of x.
Identify the value of x given in the problem, which is x = 6.2, and determine which part of the piecewise function applies to this value.
Check the conditions in the piecewise function to see where x = 6.2 fits. For example, if the function is defined as ƒ(x) = 3 for x < 4, and some other value for x ≥ 4, then since 6.2 is greater than 4, you will use the second part of the function.
Once you identify the correct piece of the function for x = 6.2, substitute x = 6.2 into that expression or use the given constant value for that interval.
Write down the value of ƒ(6.2) based on the substitution or the constant value from the piecewise function.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Function Notation and Evaluation

Function notation, written as ƒ(x), represents a rule that assigns each input x to exactly one output. Evaluating a function means substituting the given x-value into the function's rule to find the corresponding output.
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Evaluating Composed Functions

Piecewise Functions

A piecewise function is defined by different expressions depending on the input value's domain. Understanding which part of the function applies to the given x-value is essential for correctly evaluating the function.
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Function Composition

Domain and Input Values

The domain of a function is the set of all possible input values. Identifying whether the given x-value lies within the domain or specific intervals of a piecewise function helps determine which rule to use for evaluation.
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Finding the Domain of an Equation
Related Practice
Textbook Question

For each line, (a) find the slope and (b) sketch the graph. 2y = -3x

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

ƒ(x)=−x2ƒ(x)=-x^2

Textbook Question

Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

Textbook Question

For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(-3)

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Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=√(x-3)