- f(x) must then satisfy the condition that f(0) = 3. This is true only for (A) and (B).
Alternatively, by recognizing that each equation is in the slope-intercept form: f(x) = y = mx
- b, where b is the y-intercept, we can reach the same conclusion. Next, notice that the
slope of the line is positive. That is, as the value of x increases, so too does y. Returning to
the slope-intercept form, m gives the slope of the line. Only (D) has a positive coefficient
(m). Choice (D), then, is the correct function.
4. A If x + y = 0, then x = –y. Using this relationship and substituting into the expression x − y,
we find that x − y = –y – y = –2y. This is (A).
5. A This question requires factoring the expression 2x^2 – 6x − 8. Begin by factoring 2 from the
expression: 2(x^2 – 3x − 4). This expression is further factorable, giving 2(x − 4)(x + 1),
which is (A).
6. D The question describes a ramp that forms a triangle, the length of which is the hypotenuse of
the triangle. The height of the ramp (3 feet) is the length of the side of the triangle opposite
the 35° angle. In general for some angle θ, sinθ = . In the question, this
corresponds to sin35° = . This
is (D).
7. D This question requires evaluating both equations to determine the values of a and b. You
can begin by solving either of the two equations for a or b, and then substituting the solution
into the other equation. But note that the question asks for the value of a + b, so check to see
if there’s a faster way: Can you stack and add (or subtract) the equations? If you stack and
add the equations, you get 7a + 7b = 77 . Now divide both sides of the equation by 7,
resulting in a + b = 11. This is (D).
8. D When a function f(x) is transformed into a function of the form f(ax), where a is a constant,
if a > 0, the function will be compressed horizontally by a factor of a. Here, y = x^2 + 4 can
be represented as the parent function, and y = 3x^2 + 4 as the transformed function
compressed horizontally versus the parent function, and thus narrower, by a factor of 3.
This is (D). If you’re not sure, try plugging values into each equation to construct a rough
graph of each equation and compare them.
9. C Rearranging and factoring the expression provided in the question, we have t^2 – 4t – 90 = 6
t^2 – 4t – 96 = 0 (t – 12)(t + 8) = 0. Therefore, t – 12 = 0 and t + 8 = 0. t must then
equal 12 or –8. If t represents the number of tickets Steven buys, then only t = 12 is
consistent with the context of the question. If each ticket costs $80, Steven must have spent
$80 × 12 = $960. This is (C).
- C We must find values of c and d by solving the system of equations in order to determine the
