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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 51
Chapter 3, Problem 51

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

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1
Identify the function ƒ(x) given as ƒ(x) = -3x + 4.
To find ƒ(0), substitute x = 0 into the function ƒ(x).
Write the substitution explicitly: ƒ(0) = -3(0) + 4.
Simplify the expression by multiplying and adding the terms.
The result after simplification will be the value of ƒ(0).

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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 specific input value into the function's formula to find the corresponding output. For example, to find ƒ(0), replace x with 0 in ƒ(x) and simplify the expression.
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Evaluating Composed Functions

Linear Functions

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. Understanding this helps in quickly evaluating and interpreting the function's behavior for given inputs.
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Simplification of Algebraic Expressions

Simplification involves performing arithmetic operations and combining like terms to write expressions in their simplest form. This is essential after substituting values to present the final answer clearly.
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Introduction to Algebraic Expressions
Related Practice
Textbook Question

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

f(x)={5if 0<x≤220−3[[2−4x]]if x>2 , for x=5.6f(x)=\(\begin{cases}\)5 & \(\text{if }\)0<x\(\leq\)2\\ 20-3[\(\left\]\lbrack\)2-4x]\(\right\[\rbrack\) & \(\text{if }\)x>2\(\text{ }\]\end{cases}\),\(\text{ for }\)x=5.6

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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

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

Textbook Question

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

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Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4), parallel to x+3y=5