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Algebra 1 Functions Test STUDY GUIDE Name: _______________________________________ Date: __________________ Block: ___________ Algebra 1 Function Introduction STUDY GUIDE SOLs: A.7, A.4 Know how to… Plot points on a Cartesian coordinate plane. Find the (x, y) coordinates of points on the Cartesian plane. Identify the quadrant in which a point is located. Given a relation in different formats (such as a set of (x, y) pairs, mapping diagram, or graph), determine whether the relation is a function. Be able to explain why you made your choice. Remember: a relation is a function if every input has one and only one (OAOO) output. Given a relation with a discrete domain, be able to find the range of the relation. Given a graph of a relation, be able to describe the domain and range in set builder notation. Be able to graph linear equations using the table of values method and the intercept method. Be prepared to write the x- and y-intercepts in (x, y) pair form. Be able to evaluate functions that use f(x) function notation. Remember: x is the input to the function, and f(x) is the output. Be able to identify the zero of a linear function, which is the same as its x-intercept. Find it by setting the function’s output to 0, and solving for x (find x where f(x) = 0). Be able to put a linear equation into function form (solve for y). Be able to solve formulas for a given variable. Be able to use formulas created by solving for a variable in word problems. Study Questions 1) Use the graph at right to answer the questions… a) Plot and label the points P(-2, -3), Q(1, 0), R(0, 3), and S(4, -5) in the coordinate plane at right. Identify the quadrants of the points. b) Identify the coordinates of points A, B, and C. Identify the quadrants they lie in. Algebra 1 Functions Test STUDY GUIDE Page 2 2) Determine whether the relations below are functions or not. Explain how you made your choice. a) {(-4, 2), (0, -4), (4, 2), (1, -4)} b) c) d) Function? ___________ Explain: Function? ___________ Explain: Function? ________ Explain: Function? ________ Explain: 3) Given the functions below, find the range given their domain. a) y = -3x + 2 D= {-3, -2, 0, 1, 4} b) y = 1 x - 3 D= {-4, -2, 0, 1, 6} 2 4) Given the graphs below, determine whether the relations are functions. Then find the domain and range for each in set builder notation. a) b) c) d) Function? ___________ Domain _____________ Range ______________ Function? __________ Domain ____________ Range ______________ Function? __________ Function? __________ Domain ____________ Domain ____________ Range______________ Range______________ Algebra 1 Functions Test STUDY GUIDE Page 3 5) Graph the function with the given domain using the table of values method. Then identify the range of the function in set builder notation. The domain is the set of all real numbers, D = {x | x}. a) y = 4x + 3 b) y = - 1 x -1 2 6) Find the x- and y-intercepts of the graphs of the equations as ordered pairs. Then graph the functions using the intercept method. a) 3x – 2y = 12 x-intercept b) 4x – y = -8 y-intercept x-intercept 3 x+3 4 x-intercept y-intercept c) y = y-intercept 7) Evaluate the functions below. a) f(x) = -5x + 4 Find: f(1), f(-3), f(0) 3 x 7 4 Find: g(0), g(4), g(-8) b) g(x) = c) h(x) = 3x + 9 1 Find: h , h(0), h(9) 3 Find the zero of h (the x-intercept) Algebra 1 Functions Test STUDY GUIDE Page 4 8) Given f(x) = 4x – 1, complete the table below for the function. x -1 f(x) 0 3 0 7 9) Find the zero of each function (the x-intercept) below. a) f(x) = 4x + 16 b) h(x) = 2 x 10 3 10) Put the linear equations below into function form (solve for y). a) 15x + 10 = 5y b) -3x + 4y = 24 c) 3x 6y 2 12 d) 10x – 2y + 20 = 0 11) Solve each equation for the given variable. a) Solve for t: v = r + at b) Solve for x: 5xy n 6 2 c) Solve for a: 4a + b = 3a d) Solve for n: n s (a t) 2 e) Solve for c: 3x y 4 c f) Solve for C: 9 F = C+32 5 1 h(b1 b 2 ) , where b1 and b2 2 are the lengths of the bases of the trapezoid. 12) The area of a trapezoid is given by A = a) Solve the formula for h, the height of the trapezoid. b) Use the formula you created in part a above to find the height of a trapezoid if its area is 40 square inches, and its bases are 10 and 6 inches in length. Algebra 1 Functions Test STUDY GUIDE Page 5 Study Guide Answers 2) a) Yes, every input has OAOO output. 1) a) P III, Q no quadrant, R no quadrant, S IV b) A(-3, -4) III, B(0, -4) no quadrant, C(-2, 4) II b) No, input 5 has more than one output. c) Yes, every input has OAOO output. d) No, there exist inputs with more than one output. 3) a) R ={11, 8, 2, -1, -10} 5 b) R = {-5, -4, -3, , 0} 2 4) a) No; D={x | x ≥ 0}; R = {y x | y} 5) (Tables may vary depending on inputs 5b) b) Yes; D = {x | x}; R = {y | y} c) No; D = {x | -5 ≤ x < 0}; R = {y | -1 < y < 4} d) Yes; D = {x | -4 ≤ x ≤ 4}; R = {y | -3 ≤ y ≤ 4} chosen) a) 6) a) x-int: (4, 0); y-int: (0, -6) 6b) x-int: (-2, 0); y-int: (0, 8) 6c) 7) a) f(1)=-1, f(-3)=19, f(0)=4 x-int: (4, 0); y-int: (0, 3) b) g(0)=-7, g(4)=-4, f(-8)=-13 1 c) h =8, h(0)=9, h(9)=36 3 zero of h occurs at x=-3 8) 9) a) x=-4 b) x=15 10) a) y = 3x + 2 b) y 3 1 x 6 c) y x 4 4 2 d) y = 5x + 10 12) a) h 2A b) 5 inches b1 b 2 11) a) t d) n vr -12 - n b) x c) a = -b a 5y 2s 3x y 5 e) c f) C (F 32) at 4 9