Name ___________________________________ Introduction to Functions Date ___________________ Day 3 HW (1) Graph f(x) = x + 3 and g(x) = |x| + 3 on the coordinate grid below. Explain how the functions are the same and how they are different. Be specific and show all work! y 10 8 6 4 2 x -10 -8 2 -2 -4 -6 4 8 6 10 -2 -4 -6 -8 -10 (2) y = -2 x + 3 - 2 Describe the transformation(s) from y = |x|. 10 y Domain 8 Range 6 4 Increasing 2 x -10 -8 -6 -4 -2 2 4 6 8 10 -2 Decreasing Positive -4 Negative -6 -8 End Behaviors -10 (3) g(x) = 1 3 x 10 (4) When graphed on the same set of axes, in how many points do the graphs of y = |x| – 1 and y = –2 intersect? y 8 6 4 2 x -10 -8 -6 -4 -2 2 4 6 8 (1) 1 (3) 0 (2) 2 (4) 4 10 -2 -4 -6 -8 -10 Math 9R (5) The graph at the right is a transformation of the absolute value function, f(x) = |x|. a. Which of the following equations represents this graph? (1) f(x) = |x – 3| – 4 (3) f(x) = | x + 4 | – 3 (2) f(x) = | x + 3 | – 4 (4) f(x) = | x – 4 | – 3 b. For what interval is the f(x) > 0? c. What is the absolute minimum of this function? d. What is the value of f(-1) – 3f(4)? e. For what value(s) of x is f(x) = -2? For #6 – 11, write an equation for the given graphs or for the given description. Show work leading to your answer. (6) (7) (8) Write an equation for y = x left 3 units. ____________________ (9) Write an equation for y = − x up 6 units. ____________________ (10) Write an equation for y = - x down 5 units, right 3 units. ____________________ (11) Given the graph of f(x) = |x – 2| + 3, what would be the equation, g(x), for the same graph if it was translated left one unit and down two units? ____________________ Math 9R REVIEW Identify the domain and range of each relation, and determine whether the relation is a function. (12) {(3, 6), (4, 7), (5, 8), (6, 9)} (13) {(-1, 0.4), (1, 3), (-2, 1), (-1, 6)} REVIEW (CONT.) (14) Find the range of h(x) = -3x2 + 4 if the domain is {-2, 10, -1}. (15) For which of the following functions is g(-2) > g(2)? 6 (1) g(x) = 6x2 (3) g(x) = (2) g(x) = 6 (4) g(x) = 6 – x3 x (16) On the following set of axis, create the graph of a function b(x) with the following characteristics: • Domain: x ≥ -4 • Range: 0 ≤ x < 3 • b(x) > 0: x > -4 • End Behaviors: right • Is this function linear? Explain. • Is this function increasing, decreasing, or both? Math 9R

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