/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 Let \(f(x)=-3 x+4\) and \(g(x)=-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 14

Let \(f(x)=-3 x+4\) and \(g(x)=-x^{2}+4 x+1 .\) Find the following $$ f(-100) $$

Short Answer

Expert verified
f(-100) = 304

Step by step solution

01

- Understand the Problem

The task is to find the value of the function \( f(x) \) at \( x = -100 \). The function \( f(x) \) is given as \( f(x) = -3x + 4 \).
02

- Substitute the Value

Substitute \( x = -100 \) into the function, replacing all instances of \( x \) with \( -100 \). So, it becomes \( f(-100) = -3(-100) + 4 \).
03

- Simplify the Expression

Simplify the expression. First, calculate the multiplication: \( -3(-100) = 300 \). Then add 4: \( 300 + 4 = 304 \).
04

- Write the Final Answer

The value of the function \( f(x) \) at \( x = -100 \) is \( 304 \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear functions
Linear functions are one of the simplest types of functions in mathematics. A linear function can be written in the form: ewline
ewline y = mx + b , where:
  • m is the slope of the line, indicating how much y changes for a change in x.
  • b is the y-intercept, the value of y when x is 0.
  • x and y are variables.

In the given exercise, the function is written as: f(x) = -3x + 4 , which follows this format:
  • m = -3 (the slope is -3)
  • b = 4 (the y-intercept is 4).

Linear functions will always produce a straight line when graphed. Another important characteristic is that the rate of change between the x and y values is constant.
function evaluation
Function evaluation involves finding the value of a function for a specific input. For a function like f(x)=-3x+4 , this means substituting a specific value for x and calculating the result. For example, in the problem, we are asked to find f(-100) . To do this:
  • Replace x with -100 in the function expression.
  • Perform the arithmetic operations needed to determine the final value.

In our case, when x equals -100, the function becomes f(-100) = -3(-100) + 4 . The next step is to simplify this expression to get the final result, which happens to be 304. Function evaluation is a crucial concept because it allows you to determine the output of a function for any given input.
substitution method
The substitution method is a straightforward technique used in algebra to simplify expressions and solve equations. It involves replacing a variable with a specific value. In this exercise:
  • The variable x is replaced with -100.
  • The function, originally written as f(x)=-3x+4 , becomes f(-100) = -3(-100) + 4.

Breaking this down step-by-step involves:
  • Identifying the variable to be replaced (x).
  • Substituting x with -100 wherever x appears in the function.
  • Simplifying the resulting expression to find the answer.

This process helps you to handle various algebraic problems by reducing them to simple arithmetic operations.
simplifying expressions
Simplifying expressions is a fundamental aspect of algebra that involves reducing an equation or formula to its simplest form. In our problem, after substituting -100 for x, we had f(-100) = -3(-100) + 4.
The steps to simplify this are:
  • First, calculate -3(-100) . Multiplying a negative number by another negative number results in a positive number. Thus, -3(-100) = 300.
  • Next, add 4 to the result: 300 + 4.
  • This gives the final simplified result of 304.

Simplifying expressions is a key skill that allows you to make complex problems more manageable by breaking them down into simpler, more understandable parts.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Graph the union of each pair of inequalities. $$ x-2>y \text { or } x<1 $$

For each function, find (a) \(f(2)\) and (b) \(f(-1)\) $$ f=\\{(-1,3),(4,7),(0,6),(2,2)\\} $$

Graph each linear or constant function. Give the domain and range. $$ h(x)=\frac{1}{2} x+2 $$

A factory can have no more than 200 workers on a shift, but must have at least 100 and must manufacture at least 3000 units at minimum cost. How many workers should be on a shift in order to produce the required units at minimal cost? Let \(x\) represent the number of workers and y represent the number of units manufactured. The cost per worker is \(\$ 50\) per day and the cost to manufacture 1 unit is \(\$ 100 .\) Write an equation in \(x, y,\) and \(C\) representing the total daily \(\operatorname{cost} C\).

The upper deck at Guaranteed Rate Field in Chicago has produced, among other complaints, displeasure with its steepness. It is \(160 \mathrm{ft}\) from home plate to the front of the upper deck and \(250 \mathrm{ft}\) from home plate to the back. The top of the upper deck is \(63 \mathrm{ft}\) above the bottom. What is its slope?
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.