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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 55
Chapter 3, Problem 55

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

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1
Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
To find ƒ(1/3), substitute x = \(\frac{1}{3}\) into the function ƒ(x).
Write the substitution explicitly: ƒ\(\left\)(\(\frac{1}{3}\)\(\right\)) = -3 \(\times\) \(\frac{1}{3}\) + 4.
Multiply -3 by \(\frac{1}{3}\) to simplify the expression inside the function.
Add the result of the multiplication to 4 to get the simplified value of ƒ\(\left\)(\(\frac{1}{3}\)\(\right\)).

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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 formula and simplifying to find the output. For example, to find ƒ(1/3), replace x with 1/3 in ƒ(x) and simplify the expression.
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Evaluating Composed Functions

Linear Functions

A linear function has the form ƒ(x) = mx + b, where m and b are constants. Its graph is a straight line, and evaluating it involves simple arithmetic operations like multiplication and addition.
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Linear Inequalities

Simplification of Algebraic Expressions

Simplification means reducing an expression to its simplest form by performing arithmetic operations and combining like terms. This step ensures the final answer is clear and concise.
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Introduction to Algebraic Expressions
Related Practice
Textbook Question

For each line, (a) find the slope and (b) sketch the graph. 5x - 2y = 10

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)=x2+3x+1

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Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (4, 1), parallel to y=-5

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+4|

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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.See Example 4.

ƒ(x)=x2−4x+2ƒ(x)=x^2-4x+2

Textbook Question

Graph each function. Give the domain and range. ƒ(x)=[[2x]]