1. If f(x) is an even function and (6, 8) is one of the points on the graph of f(x), which reason explains why (-6, 8) must also be a point on the graph? Since the function is even, the outputs of a negative x-value and a positive x-value are the same. Since the function is even, the outputs of a negative y-value and a positive y-value are the same. The graph has rotational symmetry, so the point will be reflected across the y-axis. The graph has rotational symmetry, so the point will be rotated 90 degrees about the origin. 2. If f(x) = |x| + 9 and g(x) = -6, which describes the range of (f + g)(x)? (f + g)(x) 3 for all values of x (f + g)(x) 3 for all values of x (f + g)(x) 6 for all values of x (f + g)(x) 6 for all values of x 3. If a(x) = 2x - 4 and b(x) = x + 2, which of the following expressions produces a quadratic function? (a b)(x) (a - b)(x) (a + b)(x) 4. The value, V(m), of a comic book m months after publication has an average rate of change of -0.04 between m = 36 and m = 60. Which statement must be true? The value of the comic book decreased by a total of $0.04 between m = 36 and m = 60. The value of the comic book increased by a total of $0.04 between m = 36 and m = 60. The value of the comic book decreased by an average of $0.04 each month between m = 36 and m = 60. The value of the comic book increased by an average of $0.04 each month between m = 36 and m = 60. 5. The cost, c, of a ham sandwich at a deli varies directly with the number of sandwiches, n. If c = $54 when n is 9, what is the cost of the sandwiches when n is 3? $18 $21 $27 $48 6. Given f(x) = 10 2x, find f(7). 4 7 56 7. To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function. Is Shayla applying the vertical line test correctly? No, because the y-axis is a horizontal line. No, because using the y-axis tests only whether x = 0 is mapped to multiple values. Yes, because multiple y-intercepts represent multiple x-values being mapped to y = 0. Yes, because the y-axis represents all vertical lines of the x-values. 8. Which of the following is an even function? g(x) = (x - 1) + 1 g(x) = 2x + 1 g(x) = 4x + 2 g(x) = 2x 9. Given f(x) = 17 x, what is the average rate of change in f(x) over the interval [1, 5]? -6 -1 1 10. Given f(x) = 3x 1 and g(x) = 2x 3, for which value of x does g(x) = f(2)? x = 2 x = 5 x = 4 11. Which of the following is an odd function? f(x) = x + 5x + x f(x) = x f(x) = x + x f(x) = -x 12. If f(x) = x + x - 1 and g(x) = x, which expression is equivalent to (f - g)(x)? x - x -x + x -x + x - 1 x - x + 1 13. Russ is solving an equation where both sides are linear expressions. He sets the expressions equal to y and graphs the system finding that they are the same line. How should Russ interpret this outcome? There are no intersection points. There is exactly one intersection point. There are exactly two intersection points. There are infinitely many intersection points. 14. If f(x) = 7 + 4x and g(x) = 2x, what is the value of g(f(5))? 112 160 270 15. Mark is solving an equation where one side is a quadratic expression and the other side is a linear expression. He sets the expressions equal to y and graphs the equations. What is the greatest possible number of intersections for these graphs? none one two infinitely many 16. If f(x) = 3x - 1 and g(x) = 2x + 1, which expression is equivalent to g(f(3))? 3(6) - 1 2(5) + 1 2(6) + 1 3(3) - 1 2(3) + 1 g(5) - 1 g(5) + 1 17. If f(x) = (x + 9), which statement about f(x) is true? f(x) is an even function for all values of x. f(x) is an even function for all even values of x. f(x) is an odd function for all values of x. f(x) is an odd function for all odd values of x. 18. Heather is solving an equation by graphing the expressions on either side of the equal signs. If the graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve? One side of the equation is a constant, and the other side is a linear expression. One side of the equation is a linear expression, and the other side is a quadratic expression. One side of the equation is a constant, and the other side is a quadratic expression. One side of the equation is a quadratic expression, and the other side is a quadratic expression