Question

In Exercises, explain the mistake that is made. Given the functions $f(x)=|x-A|-1$ and $f(1)=-1,$ find $A$ Solution: since $f(1)=-1,$ the point $(-1,1) \quad-1=|-1-A|-1$ must satisfy the function. Add 1 to both sides of the equation. $\quad|-1-A|=0$ The absolute value of zero is zero, so there is no need for the absolute value signs: $-1-A=0 \Rightarrow A=-1$ This is incorrect. What mistake was made?

Name: Problem 110, Chapter 1: Precalculus
Uploaded: 2020-06-30T20:26:41-08:00
Duration: 54 s
Channel: Dale Sanford
Description: In Exercises, explain the mistake that is made. Given the functions f(x)=|x-A|-1 and f(1)=-1, find A Solution: since f(1)=-1, the point (-1,1) -1=|-1-A|-1 must satisfy the function. Add 1 to both sides of the equation. |-1-A|=0 The absolute value of zero is zero, so there is no need for the absolute value signs: -1-A=0 ⇒A=-1 This is incorrect. What mistake was made?

   In Exercises, explain the mistake that is made.
Given the functions $f(x)=|x-A|-1$ and $f(1)=-1,$ find $A$
Solution:
since $f(1)=-1,$ the point $(-1,1) \quad-1=|-1-A|-1$
must satisfy the function.
Add 1 to both sides of the equation. $\quad|-1-A|=0$
The absolute value of zero is zero, so there is no need for the absolute value signs: $-1-A=0 \Rightarrow A=-1$
This is incorrect. What mistake was made?

Precalculus

Cynthia Young 2nd Edition

Chapter 1, Problem 110

Instant Answer

Solved by Expert Dale Sanford

06/30/2020

Step 1

This means that when we substitute $x=1$ into the function $f(x)$, the result should be $-1$. So, we substitute $x=1$ into the function $f(x)$ to get $-1=|1-A|-1$. Show more…

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In Exercises, explain the mistake that is made. Given the functions $f(x)=|x-A|-1$ and $f(1)=-1,$ find $A$ Solution: since $f(1)=-1,$ the point $(-1,1) \quad-1=|-1-A|-1$ must satisfy the function. Add 1 to both sides of the equation. $\quad|-1-A|=0$ The absolute value of zero is zero, so there is no need for the absolute value signs: $-1-A=0 \Rightarrow A=-1$ This is incorrect. What mistake was made?

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Key Concepts

Absolute Value Equations

Understanding and solving absolute value equations is crucial when the equation involves expressions like |x - A|. The property that |y| = 0 if and only if y = 0 must be applied carefully. Errors often occur when the argument of the absolute value is misidentified or when the properties of absolute values are improperly used in the algebraic manipulation process.

Function Evaluation

This concept involves substituting a given input into the function accurately. In problems where a function is defined with parameters, correctly replacing the variable with the provided input is essential to obtaining the right equation to solve for unknowns. A mistake in this step, such as using the wrong input value or misinterpreting the function's definition, can lead to an incorrect solution.

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