Name the subsets of the real number square root 34
1 answer:
You might be interested in
9514 1404 393
Answer:
(d) see below
Step-by-step explanation:
Since each grid square is 1/4 unit. the coordinates in terms of grid squares are ...
A(0.50, -1.25) ⇒ (0.50/.25, -1.25/.25) = (2, -5) . . . grid squares
Point A is located 2 squares right and 5 squares down on the grid. This matches choice D.
It looks like you have the domain confused for the range! You can think of the domain as the set of all "inputs" for a function (all of the x values which are allowed). In the given function, we have no explicit restrictions on the domain, and no situations like division by 0 or taking the square root of a negative number that would otherwise put limits on it, so our domain would simply be the set of all real numbers, R. Inequality notation doesn't really use ∞, so you could just put an R to represent the set. In set notation, we'd write
and in interval notation,
The <em>range</em>, on the other hand, is the set of all possible <em>outputs</em> of a function - here, it's the set of all values f(x) can be. In the case of quadratic equations (equations with an x² term), there will always be some minimum or maximum value limiting the range. Here, we see on the graph that the maximum value for f(x) is 3. The range of the function then includes all values less than or equal to 3. As in inequality, we can say that
,
in set notation:
(this just means "f(x) is a real number less than or equal to 3")
and in interval notation:
The interval notation is
Explanation:
The inequality is
Let us complete the square, we get,
Simplifying, we have,
Adding both sides of the equation by 11, we get,
Since, we know that for , if n is even then
Thus, writing the above expression in this form, we get,
Also, if then
and
Then ,we have,
and
Solving the inequalities, we get,
and
Merging the intervals, we have,
Hence, writing the solution in interval notation, we have,
Therefore, the answer is