<p>If |ax-1|≤1, where a is a positive even integer,
which of the following cannot be a value of x^2.</p>
<p>a.0
b. 1/4
c. 1/2
d. 1
e. 4</p>
<p>The function f is defined by f(x)= 2x^2-5. What are all possible values of f(x)
where -2 < x< 2?</p>
<p>a. -5≤ f(x) < 0
b. -5≤ f(x)<3
c.0≤f(x)< 8
d. 0≤f(x)<8
e. 2≤f(x)<8</p>
<p>Each of the 75 children in a line was assigned one of the integers from 1 through 75 by counting off in order. Then, standing in the same order, the children counted off in the opposite direction, so that the child who was assigned the number 75 the first time was assigned the number 1 the second time. Which of the following is a pair of numbers assigned to the same child?</p>
<p>a. 50 and 25
b. 49 and 24
c. 48 and 26
d. 47 and 29
e. 45 and 32</p>
<ol>
<li>-1 ≤ ax - 1 ≤ 1 → 0 ≤ ax ≤ 2. Divide both sides by a (note that inequality sign does not switch) to obtain</li>
</ol>
<p>x ≤ 2/a → x^2 ≤ 4/(a^2). a is a positive even integer so clearly a is at least 2, and the largest possible value of 4/(a^2) is 1, when a = 2. Therefore it is impossible for x^2 to equal 4, E.</p>
<ol>
<li><p>Helps to draw/visualize a graph of f. Clearly, the minimum value of f is -5 at x = 0, and the maximum value occurs at x = 2 or -2 (which is 3). So -5 ≤ f(x) ≤ 3 along the domain, B.</p></li>
<li><p>1 2 3 … 75 becomes
75 74 73… 1</p></li>
</ol>
<p>So the first child received 1 and 75, the second received 2 and 74, and so on. Note that the sum of the numbers given to each child is always 76. Only choice D has two numbers adding up to 76, so this is the answer.</p>