Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 48

Chapter 3, Problem 48

Find the value of the function for the given value of x. ƒ(x)=[[3-(x/2)]], for x=1

Verified step by step guidance

Identify the given function and the value of $ x $. The function is $ f(x) = \left\lfloor 3 - \frac{x}{2} \right\rfloor $ and $ x = 1 $.

Substitute the value of $ x = 1 $ into the function: $ f(1) = \left\lfloor 3 - \frac{1}{2} \right\rfloor $.

Simplify the expression inside the floor function: calculate $ 3 - \frac{1}{2} $.

Evaluate the floor function $ \left\lfloor \cdot \right\rfloor $, which means finding the greatest integer less than or equal to the simplified value.

Write the final expression for $ f(1) $ after applying the floor function, which gives the value of the function at $ x = 1 $.

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Key Concepts

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

Function Evaluation

Function evaluation involves substituting a given input value into the function's expression and simplifying to find the output. For example, if ƒ(x) = 3 - (x/2), to find ƒ(1), replace x with 1 and simplify the expression.

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). Correctly applying this ensures accurate simplification of expressions.

Floor Function (Greatest Integer Function)

The floor function, denoted by [[x]], returns the greatest integer less than or equal to x. For example, [[2.7]] = 2 and [[-1.3]] = -2. Understanding this helps interpret the function ƒ(x) = [[3 - (x/2)]] correctly.

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Function Composition

Related Practice

Textbook Question

Find the slope of each line, provided that it has a slope. through (2, -2) and (3, -4)

Textbook Question

Graph the line satisfying the given conditions. through (2, -4), m = 3/4

Textbook Question

Work each of the following. Find the equation of a circle with center at (-4, 3), passing through the point (5, 8).Write it in center-radius form.

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Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. y=-7/(x-5)

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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)=1/x

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.

$ƒ (x) = - 4 x + 2$