please help w/ Q's regarding fncs, domain, and range

danlail07

New member
Joined
Sep 6, 2006
Messages
2
I am a 41 year old college student trying to get his math requirement out of the way, and I have not taken a math class since 1985. I have a few questions that I need help with, and I would appreciate any input.

1) T or F: The domain for the function -4x+6 is (-00,00), and the range is (-00,6)

2) T or F: The domain of x^2+2 is (-00,00), and the range is (2,00)

I have never seen anything like this. Could I get an explanation?

Just for good measure, let me throw this one in:

What is the distance between the points (3,17) and (-2,5)

Thanks in advance!!
 

soroban

Elite Member
Joined
Jan 28, 2005
Messages
5,588
Re: Please help, I am struggling!!!

Hello, danlail07!

The domain is the set of all possible (legal) values of \(\displaystyle x.\)

The range is the set of all resulting values of \(\displaystyle y.\)


1) T or F: The domain for the function \(\displaystyle \,-4x\,+\,6\) is \(\displaystyle (-\infty.\,\infty)\), and the range is \(\displaystyle (-\infty,\,6)\)

False

The statement about the domain is true . . . \(\displaystyle x\) can be any real value.

But the starement about the range is falce.
The range is also all real values: \(\displaystyle (-\infty,\,\infty)\)



2) T or F: The domain of \(\displaystyle x^2\,+\,2\) is \(\displaystyle (-\infty,\,\infty)\) and the range is \(\displaystyle (2,\,\infty)\)

Is this is a Trick Question?

The range is: \(\displaystyle \,[2,\,\infty)\) . . . the "2" is included.


\(\displaystyle x\) can be any real number.

Recall that \(\displaystyle \,y\:=\:x^2\,+\,2\) is an up-opening parabola.
It "bottoms out" at its vertex, which is at \(\displaystyle (0,\,2)\).
. . That is, the minimum value of \(\displaystyle y\) is 2.
Hence, the range is: \(\displaystyle \,[2,\,\infty)\)



Find the distance between the points (3,17) and (-2,5)/

You're expected to know the Distance Formula.

The distance between \(\displaystyle P(x_1,y_1)\) and \(\displaystyle Q(x_2.y_2)\) is:

. . . \(\displaystyle d\;=\;\sqrt{(x_2\,-\,x_1)^2\,+\,)y_2\,-\,y_1)^2}\)


Your points are: \(\displaystyle \,(3,\,17)\) and \(\displaystyle (-2,5)\)

\(\displaystyle d\;=\;\sqrt{(-2\,-\,3)^2\,+\,(5\,-\,17)^2} \;=\;\sqrt{(-5)^2\,+\,(-12)^2} \;=\;\sqrt{25\,+\,144}\;=\;\sqrt{169}\;=\;13\)

 
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