<p>page 674 #20 from blue book. It has a chart on it but this is the question:</p>
<p>The figures above show the graphs of the functions of f and g. 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?</p>
<p>(A) -6
(B) -3
(C) -2
(D) 3
(E) 6</p>
<p>I know the long way to do it, but I don't think SAT would ask a 5 minute math problem on the test. So what is the more easier and efficient way to approach this problem?</p>
<p>BTW the graph for f has the points (-1,3) and (1,-3) labed on the graph and for graph g, it has the points (2,1) and (4,-5). Thanks</p>
<p>g(x) is defined at x = 2 (= -1 + 3) and x=4 (= 1 + 3) i.e. the x values are each 3 units greater than the values where f(x) is defined. So h=3 is one possible value.</p>
<p>g(2) = 1 = 2 units LESS than f(-1)
and g(4) = -5 = 2 units LESS than f(1) .
So k= -2 is a possible value for k.</p>
<p>the answer is E according to the blue book. Theres a very simple way of solving it. </p>
<p>Any constant that is added to 'x' causes the graph to shift to the left or right that many units. For istance if we have the function f(x), then f(x+2) will be the same graph shifted two units to the left of the x axis. If the constant is a negative number, the graph shifts twice to the right.</p>
<p>now if we have the same function f(x), then f(x)+2 would shift two units upwards. f(x)-2 will shift two units downwards.</p>
<p>something like that. Check out some calc book to find these rules.</p>
