Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 44

Chapter 3, Problem 44

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

Verified step by step guidance

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.

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.

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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Related Practice

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=1-x

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. y=-√x

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Textbook Question

The graph of a linear function f is shown. (a) Identify the slope, y-intercept, and x-intercept. (b) Write an equation that defines f.

Textbook Question

The graph of y=|x-2| is symmetric with respect to a vertical line. What is the equation of that line?

Textbook Question

Graph each equation.

$f with hook x equals 3$

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Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=2-x