/*! 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 89 Given the following, \(g(x)=12... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 89

Given the following, \(g(x)=12 x-13,\) find \(g(-13)\)

Short Answer

Expert verified
\(g(-13) = -169\).

Step by step solution

01

Identify the Function and Input

The function given is \(g(x) = 12x - 13\). We need to evaluate this function at \(x = -13\).
02

Substitute the Input into the Function

Replace \(x\) in the function \(g(x)\) with \(-13\). This gives us \(g(-13) = 12(-13) - 13\).
03

Perform the Multiplication

Calculate the result of the multiplication: \(12 \times (-13) = -156\).
04

Solve the Expression

Using the result from Step 3, complete the expression: \(g(-13) = -156 - 13\).
05

Final Calculation

Subtract the numbers: \(-156 - 13 = -169\). Hence, \(g(-13) = -169\).

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 a simple yet powerful type of function in mathematics. These functions are defined by equations of the form \(f(x) = ax + b\), where \(a\) and \(b\) are constants.
In our exercise, the function is \(g(x) = 12x - 13\), which is a classic example of a linear function. Here, \(12\) is the coefficient of \(x\), and \(-13\) is the constant term, or y-intercept.
  • The coefficient \(a = 12\) determines the slope of the line. A positive slope means the line inclines upwards, while a negative one means it declines.
  • The constant \(b = -13\) shifts the entire line up or down on a graph.
Understanding the components of linear functions helps in graphing them and predicting their behavior. Linear functions are foundational in algebra and used to model relationships where the change is constant.
Substitution
Substitution is a method used to evaluate functions at specific points. It involves replacing a variable with a given number. In our exercise, we're asked to find \(g(-13)\). This means we substitute \(-13\) in place of \(x\) in the function \(g(x)=12x-13\).
The process is as follows:
  • Take the original function \(g(x) = 12x - 13\).
  • Replace \(x\) with \(-13\), resulting in the expression \(g(-13) = 12(-13) - 13\).
This technique simplifies the function to allow for direct computation. Substitution is a crucial step in function evaluation, enabling the calculation of function values for particular inputs.
Arithmetic Operations
Arithmetic operations refer to basic mathematical calculations such as addition, subtraction, multiplication, and division. In our step-by-step solution, we mainly perform multiplication and subtraction.
After substitution, the task requires finding \(12 \times (-13)\). Understanding multiplication of positive and negative numbers is key:
  • Multiplying a positive by a negative results in a negative product: \(12 \times (-13) = -156\).
  • The next step involves subtraction: \(-156 - 13\), which further decreases the number.
Subtraction of a positive number from a negative number involves moving left on the number line, leading to \(-169\) in our exercise. Mastering these operations is essential for evaluating functions and solving equations.

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 using the slope and \(y\) -intercept. $$ y=0 $$

Find at least five ordered pair solutions and graph. $$ 2 x-3 y=12 $$

Given the following, \(f(x)=9 x-4,\) find \(f(-1)\)

Find the equation of the line given two points on the line. \((5 / 2,-2)\) and \((-5,5 / 2)\)

Find the equation of the line in slope-intercept form. Perpendicular to \(y=1\) and passing through (4,-1) .
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.