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

#### danlail07

##### New member
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)

#### soroban

##### Elite Member

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 $$\displaystyle (-2,5)$$

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