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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 52
Chapter 3, Problem 52

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

Verified step by step guidance
1
Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
To find ƒ(-3), substitute -3 in place of x in the function ƒ(x).
Write the substitution explicitly: ƒ(-3) = -3( -3 ) + 4.
Simplify the expression by performing the multiplication and then the addition.
The result after simplification will be the value of ƒ(-3).

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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(-3), replace x with -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. It produces a straight-line graph, and evaluating it at any x involves simple arithmetic operations like multiplication and addition.
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Linear Inequalities

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents, combined using addition, subtraction, and multiplication. Understanding how to substitute values and simplify polynomials is essential for evaluating functions like g(x).
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Introduction to Polynomial Functions
Related Practice
Textbook Question

Find the value of the function for the given value of x.

f(x)={3if 0<x≤410−2[[5−x]]if x>4, for , for x=6.2f(x)=\(\begin{cases}\)3 & \(\text{if }\)0<x\(\leq\)4\\ 10-2[\(\left\]\lbrack\)5-x]\(\right\[\rbrack\) & \(\text{if }\)x>4,\(\text{ for }\]\end{cases}\),\(\text{ for }\)x=6.2

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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)=−x2ƒ(x)=-x^2

Textbook Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. y=x2

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Textbook Question

Find the slope of each line, provided that it has a slope. through (5, 6) and (5, -2)

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(0)

Textbook Question

For each line, (a) find the slope and (b) sketch the graph. y = 2x - 4