Write out the following proportions in words. a. 7 : 28 = 2 : 8 b. 3⁄1 = 18⁄6 c. 9 : 72 = 2 : 16 d. 81⁄9 = 45⁄5

1) Proportion a.

7 : 28 = 2 : 8

That means that the ratio 7 / 28 is equal to the ratio 2 : 8. 

You can verify the equality by simplifying to the simplest form:

     7 : 28 = 1 / 4 simplest form
     2 : 8 = 1 / 4 simplest form, then the proportion is right.

In words that is 7 is to 28 as 1 is to 4 ← answer

2) Proportion b.. 3⁄1 = 18⁄6


In words: 3 is to q as 18 is to 6 ← answer


You can verify the proportion by simplifiying the second fraction:


     18 / 6 = [18 / 6] / [ 6 / 6] = 3 / 1


3) Proportion c. 9 : 72 = 2 : 16


In words: 9 is to 72 as 2 is to 16 ← answer


Proove the proportion:


     9 / 72 = 1 / 8


     2 / 16 = 1 / 8


4) Proportion d. 81⁄9 = 45⁄5

In words: 81 is to 9 as 45 is to 5 ← answer

Proove it: 
      81 / 9 = 9
      45 / 9 = 9

We can not see the graph, but that does not matter.

For a function y = f(x), the domain is the set of the possible values of x that we can input in the function, and the range is the set of the possible outputs.

First, for the domain, we start assuming that the domain is the set of all real numbers.

Then we look at our function, there is a point that causes a problem?

(a problem can be a zero in a denominator, for example)

Well, we have a quadratic equation, then we can not have any "x" in a denominator, then there are not problems, which means that the domain is the set of all real numbers.

For the range we first need to find the minimum (or maximum value) of f(x).

Here we know that the vertex is (1, - 3)

If the arms of the graph open upwards, then the minimum is at the vertex, which means that the minimum value of y is y = -3

And the arms go upwards infinitely, so there is no upper limit.

Then the range is the set of all numbers such that:

-3 ≤ y

Now, if the arms of the graph open downwards, then the maximum is at the vertex, which means that the maximum of our function is at y = -3

And with similar thinking than in the above case, we can find that the range is:

R:  y ≤ -3.