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

[danlail07]

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]

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 $\displaystyle (-2,5)$

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