Problem Set D: y g(x) = ( 2 x − 3)1 4 + 1 1. In the function above, for what values of x is g(x) a real number? (A) x ≥ 0 (B) x ≥ 1/2 (C) x ≥ 3/2 (D) x ≥ 2 (E) x ≥ 3 (–1, 0) 5. 2. x –1 0 1 2 f(x) 1 3 1 –5 The table above shows the values of the quadratic function f for several values of x. Which one of the following best represents f? (A) (B) f (x) = −2 x 2 2 f (x) = x + 3 2 (C) f (x) = − x + 3 (D) f (x) = −2 x 2 − 3 (E) 2 In the function above, if f(k) = 2, then which one of the following could be a value of k ? (A) –1 (B) 0 (C) 0.5 (D) 2.5 (E) 4 Let the function h be defined by h(x) = x + 2 . If 3h(v) = 18, then which v one of the following is the value of h ? 4 (A) –4 (B) –1 (C) 0 (D) 2 (E) 4 (B) x = − y2 (C) x = − y2 + 1 (D) x = y2 − 1 (E) x = ( y + 1) 2 2 At time t = 0, a projectile was fired upward from an initial height of 10 feet. Its height after t seconds is given by the function h(t) = p − 10(q − t) 2 , where p and q are positive constants. If the projectile reached a maximum height of 100 feet when t = 3, then what was the height, in feet, of the projectile when t = 4 ? (A) 62 (B) 70 (C) 85 (D) 89 (E) 90 y = f (x) 4. x = − ( y + 1) 7. y 3. (A) A pottery store owner determines that the revenue for sales of a particular item can be modeled by the function r(x) = 50 x − 40, where x is the number of the items sold. How many of the items must be sold to generate $110 in revenue? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 f (x) = −2 x + 3 x The graph above shows a parabola that is symmetric about the x-axis. Which one of the following could be the equation of the graph? 6. 2 1 x O y A D O 8. y = a − x2 B C x The figure above shows the graph of y = a − x 2 for some constant a . If the square ABCD intersects the graph at points A and B and the area of the square is 16, what is the value of a ? (A) 2 (B) 4 (C) 6 (D) 8 (E) 10