<p>Can anybody explain these two questions from the blue book:</p>
<p>PRACTICE TEST #5</p>
<p>-->Section 3 #17</p>
<p>If p, r, and s are three different prime numbers greater than 2, and n = p x r x s, how many positive factors, including 1 and n, does n have?
- the question looks deceptively simple - the answer is 8</p>
<p>-->Section 7 #20
There's two graphs become shown; one graph is y=f(x) with points (-1,3) and (1,-3) given while the other graph is y=g(x) with points (2,1) and (4,-5) given.</p>
<p>The figures above show the graphs of the functions 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>If p, r, and s are three different prime numbers greater than 2, and n = p x r x s, how many positive factors, including 1 and n, does n have?
- the question looks deceptively simple - the answer is 8</p>
<p>The answer is also deceptively simple. Imagine some integer j that divides n. j's prime factorization can only include the primes that factorize to n. We have 3 different numbers, of which we can choose to either include or exclude either. So 2 choices for each one, and 3 total choices. 2^3=8</p>
<p>-->Section 7 #20
There's two graphs become shown; one graph is y=f(x) with points (-1,3) and (1,-3) given while the other graph is y=g(x) with points (2,1) and (4,-5) given.</p>
<p>The figures above show the graphs of the functions 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>I definitely need to see the graph for this one.</p>
<p>okay for #20, you should know the rules of transformation- shift to the left, right, up down, stretch, shrink. If you move to the right, then h is negative. so h in this case would be -3. As for k or the number of shifts up/down, it is -2 (3-1). hk = 6.</p>
<p>you have
1, p, r, s, and n. but wait, they say p, r, and s are prime factors, meaning you can also get "grouped up"
so you have to add pr, ps, rs.</p>
<p>so you get 8.</p>
<hr>
<p>john, no you don't.</p>
<p>f(-1,3); g(2,1)</p>
<p>to get from -1 to 2, you need to move to the right 3 times (value is -3)
to get from 3 to 1, you need to move down 2 times (value is -2)</p>
<p>-3 x -2 = 6</p>
<p>all you need to know is that
f (x+h) + k</p>
<p>h moves the graph to the right(- value) or left (+ value)
k moves the graph down(- value) or up(+ value)</p>