<p>(BB, pg673) 18. If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?</p>
<p>I actually got this question right because I had enough time left (~10 minutes) to enter every integer in my calculator. I was just curious whether or not there was a faster way to do this problem.</p>
<p>(Section 7, BB, pg674) 20. (look at graphs) The function f is defined by f(x) = x^3 - 4x. The function g is defined by g(x) = f(x+h) + k, where h and k are constants. What is the value of hk? I know you can get the answer by finding the horizontal and vertical shifts, but I don't get why is can be applied to the equation g(x). Explanation please?</p>
<p>Note that it is an arithmetic progression where first term is -22 and common difference is 1.
Let the number of terms be N.
N/2 x [2(-22) + (N-1)(1)] = 72
N works out to be 48.
X - (-22) + 1 = 48
x = 25</p>
<p>The quick way is to notice that the integers from -22 to +22 add up to zero . Then, 3 more integers — 23, 24 and 25 add up to the desired total of 72. So the last of them is 25.</p>
<p>Nevermind, it is understood. LOL.</p>
<p>For question 20, you have to recognize that f(x) and g(x) are the same graphs (but translated).</p>
<p>From there, you just have to see the translation. From g(x) to f(x) the graph moves 3 to the left and 2 up. </p>
<p>In the equation g(x) = f(x+h) +k, the h represents the horizontal shift and the k represents the vertical shift. That would make h= 3 and k = 2.</p>