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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 44
Chapter 3, Problem 44

Find the value of the function for the given value of x. ƒ(x)=[[0.5x]], for x=7

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Identify the function given: \( f(x) = \lfloor 0.5x \rfloor \), where \( \lfloor \cdot \rfloor \) denotes the floor function, which means rounding down to the nearest integer.
Substitute the given value \( x = 7 \) into the function: \( f(7) = \lfloor 0.5 \times 7 \rfloor \).
Calculate the product inside the floor function: \( 0.5 \times 7 = 3.5 \).
Apply the floor function to \( 3.5 \), which means finding the greatest integer less than or equal to \( 3.5 \).
The result of the floor function is the value of \( f(7) \).

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Key Concepts

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

Function Notation

Function notation, written as ƒ(x), represents a rule that assigns each input x to exactly one output. Understanding this notation helps interpret the problem as finding the output value when a specific input is given.
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Interval Notation

Floor Function

The floor function, denoted by [[x]], returns the greatest integer less than or equal to x. It essentially rounds down any decimal or fractional value to the nearest whole number below or equal to it.
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Function Composition

Evaluating Functions at a Given Input

Evaluating a function at a given input means substituting the input value into the function's expression and simplifying. This process involves performing arithmetic operations and applying any special functions, like the floor function, to find the output.
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Evaluating Composed Functions
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