Absolute Value & Function

[Vertciel]

Hello everyone,

I have 2 questions which I would appreciate if someone could answer. Thank you very much!

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1. Dave can mow his lawn in 20 minutes less time with his power mower than with his hand mower. One day his power mower broke down 15 minutes after he started mowing, and he needed 25 minutes more time to completeh the job with his hand mower. How many minutes does Dave take to mow the lawn with the power mower?

I set up the following equation: \(\displaystyle \frac{15}{x}\ + \frac{25}{x + 20}\ = 1\), which gave me \(\displaystyle x = 30\). The answer was \(\displaystyle x = 50\) and the equation in the answer key was \(\displaystyle \frac{15}{x - 20}\ + \frac{25}{x}\ = 1\).

Why doesn't my equation work?

2. The graph below represents the graph of y = f(x). Which is the graph of y = f(-x)?

I don't understand why the graph of y = f(-x) is exactly the same as y = f(x).

The graph can be found here:

 

[stapel]

1) What does "x" stand for? What reasoning did you use in creating your equation?

2) On what basis did you conclude that f(-x) has the same graph as f(x)?

Thank you!

Eliz.

 

[Deleted member 4993]

Hello everyone,

I have 2 questions which I would appreciate if someone could answer. Thank you very much!

---

1. Dave can mow his lawn in 20 minutes less time with his power mower than with his hand mower. One day his power mower broke down 15 minutes after he started mowing, and he needed 25 minutes more time to completeh the job with his hand mower. How many minutes does Dave take to mow the lawn with the power mower?

I set up the following equation: \(\displaystyle \frac{15}{x}\ + \frac{25}{x + 20}\ = 1\), which gave me \(\displaystyle x = 30\). The answer was \(\displaystyle x = 50\) and the equation in the answer key was \(\displaystyle \frac{15}{x - 20}\ + \frac{25}{x}\ = 1\).

Why doesn't my equation work?

2. The graph below represents the graph of y = f(x). Which is the graph of y = f(-x)?

I don't understand why the graph of y = f(-x) is exactly the same as y = f(x).

The graph can be found here:

The book found the time taken by the hand mower.

According to the problem posted - you are correct.

For the graph - the curve shown is similar to that of y = x^3

So the answer should be (4) where f(-x) = - f(x)

 

[tkhunny]

1) It is all in the definition. Whether one i sx and the other x+20, or one is x and the other x - 20, it is of no consequence, but one must WRITE DOWN these definitions and remember them. Whichever way it goes, the power mower is 30 min and the hand mower is 50 min. If the answer key says x = 50 is correct, either the answer key is wrong or the question is wrong. It can't be neither. Maybe it meant to ask about the hand mower.

2) Are you saying the book says the correct answer is "3"? That is not correct.

 

[Vertciel]

Thank you for your replies and clarification. This book has a lot of faulty answers.

1. The book actually gave the answer for the hand mower, when it was supposed to give the answer for the power mower. That was why I didn't get the correct answer.

2. The book gave (3) as the correct answer, when it was supposed to be (4).