Find the domain and range of

f(x)= (2x+6) / ((x^2)-x-12)

Step-by-step explanation:

If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away.  If there is, this affects the domain.  The domain are the values in the denominator that the function covers as far as the x-values go.  If we factor both the numerator and denominator, we get this:

Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away.  That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x.  The other factor, (x - 4), does not cancel out.  This is called a vertical asymptote and affects the domain of the function.  Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4.  That means that the function has to split at that x-value.  It comes in from the left, from negative infinity and goes down to negative infinity at x = 4.  Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity.  The domain is:

(-∞, 4) U (4, ∞)

The range is (-∞, ∞)

If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.

the correct answer is b) histograms can be used to exhibit the shape of distributions. this is because histograms count the frequency of each possible answer, so one is able to see which results are more common and which are less common.

1. minimum

2. 6400

3. eight

hope this !