Ch. 2 - Graphs and Functions

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

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 47

Chapter 3, Problem 47

Find the value of the function for the given value of x. ƒ(x)=[[x/4]], for x=7

Verified step by step guidance

Identify the function given: $ f(x) = \left\lfloor \frac{x}{4} \right\rfloor $, where $ \left\lfloor \cdot \right\rfloor $ denotes the floor function, which means rounding down to the nearest integer.

Substitute the given value $ x = 7 $ into the function: $ f(7) = \left\lfloor \frac{7}{4} \right\rfloor $.

Calculate the division inside the floor function: $ \frac{7}{4} $.

Apply the floor function to the result of the division, which means take the greatest integer less than or equal to $ \frac{7}{4} $.

Write the final expression for $ f(7) $ as the floor of $ \frac{7}{4} $ and interpret the value accordingly.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 value of x into the function's expression and simplifying to find the output.

Floor Function (Greatest Integer Function)

The floor function, denoted by [[x]], returns the greatest integer less than or equal to x. For example, [[3.7]] = 3 and [[-1.2]] = -2. It essentially 'rounds down' to the nearest whole number.

Order of Operations

When evaluating expressions, follow the order of operations: parentheses, exponents, multiplication and division (left to right), then addition and subtraction (left to right). This ensures correct simplification before applying the floor function.

Recommended video:

Guided course

8:38

Performing Row Operations on Matrices

Related Practice

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

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=-2x+5

Textbook Question

Graph the line satisfying the given conditions. through (0, 5), m= -2/3

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.

$ƒ (x) = 4 x + 11$

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. y=√(7-2x)

views

Textbook Question

Find the value of the function for the given value of x. ƒ(x)=2-[[-x]], for x=3.7

views