Functions and Their Graphs Worksheet Answers

ALGEBRA 2 Name: KEY Date: 2.1 Functions and Their Graphs Vocabulary: Relation: a mapping (or pairing) of input values with output Domain: the set of input values input Function: a special type of relation in which each has EXACLY ONE In other words, a function can NOT have any repeating x-values! output values Range: the set of output values Identify the domain & range. State whether each relation is a function by writing "yes" or "no". 1) Input Output 2) Input Output -2 2 Domain: \{- 2, 1, 4\} -3 1 1 Range: \{- 3, 1, 2, 3\} 4 3 -3 -1 -2- 1 Domain: \{- 3, - 2, 1, 4\} Range: \{- 3, - 1, 1\} 1 4 -3 Function: Yes each input has exactly one output Practice for you: 3) Input Output 2 4 1 -1 2 3 Function: No the input value of I gives two different outputs, -31 4) Input Output -3 22 5) Input Output -2 0 2 Domain: \{- 1, 2, 3, 4\} Range: \{- 2, 1\} Function: Yes Vertical Line Test 3 Domain: \{0, 2, 3\} 1 4 Range: \{1, 2, 3\} Function: No Domain: \{- 2, 0, 2, 4\} Range: \{- 4\} Function: Yes A relation is a function if and only if NO vertical line intersects the graph of the relation at more than one point. Are the following graphs functions? 6) 7) 8) 9) 10) Yes No No Yes Yes (- 4, - 1) 11) Plot the points for this relation on a graph. Use the VLT to determine if the relation is a function. Input Output 1 2 Graphing Functions Use a t-chart to graph the following equations. No! →fails at x=-2 12) y = x + 1 input output 13) y = - x + 4 Y X 1- 0 5 0 1 4 2 22 14) y = x - 3 15) y = 2x + 3 X Y -2-5 0-3 2-1 Practice Multiple Choice: -1 1 03 15 Multiple Choice What is the domain of the relation shown below! A 0. 1.2.3 (3.5). (2-2), (1, 5), (0-2), (1, 2) B-2,2,5 C0.2.3 Multiple Choice Which point lies on the graph of y = 8x =2? -2, 0, 1, 2, 3, 5 182 (8.) H (2.14) 12. 762 14 Multiple Choice Which ordered pair is included in the function represented by the diagram? Input -53 Output (-5,3) A (-5.0) B) (0.3) 0- 5 5- (5.3) D (5,5) 10 7 (10,7) (0, 5) ALGEBRA 2 Name: KEY Date: 2.2 Linear Functions and Function Notation Vocabulary: A linear function has the form. sqrt(mx + b) where and b are constants (numbers). For example: y = 2x + 1 The graph of a linear function is a For example: f(x) = 2x + 1 line We can use function notation. f(x) is the same asy! ( f(x) is pronounced: "/of x".) Are each of the following functions linear? Explain. 1) f(x) = 4x - 1 b=-1 Evaluating Functions 2) g(x) =5-x^ ominus No -> Con + roM * 2 Evaluate the function when x = 3 5) f(x) = 4x - 1 =11 f(3) = 4(3) - 1 Application 6) g(x) = - 2x ^ 2 + 5 =-18+5 g(3) = - 2 * (3) ^ 2 + 5 = boxed - 13 3) can't be in the denominator! h(x) = 9/6 4) r(x) = x/9 = 1/9 * x' + 0 ks -> m = 1/9, b = 0 7) p(x) = x ^ 2 + 3x + 8 p(3) = 3 ^ 2 + 3(3) + 8 = 9 + 9 + 8 = boxed 26 8) You want to join a local fitness club. The club charges a one-time membership fee of $60 and a monthly fee of $50, $50 per month a) Write a function that models your total membership cost. f(x) = 60 + 50x b) Use the function to find the cost of membership for the first year. X=12 (12 months in a year) f(12) = 60 + 50(12) $660 = 60 + 600 Practice Multiple Choice: Multiple Choice Which of the following is a linear function? Multiple Choice What is the value of f(x) = x ^ 2 + 2x - 3 when.x x =-3? f(- 3) = (- 3) ^ 2 + 2(- 3) - 3 F-3 -1 H0 Multiple Choice What function is shown in the graph? 3 x(x) = 2x + 1 Multiple Choice The function d(t) 0.125t models the distance in miles a jogger runs in minutes. How many miles does the jogger run in half an hour? t = 30 0.0625 mi 3.75 ml 6.25 mi 1-2-3 7.5 mi (0,1) d(30) = 0.125(30) A f(x) = x ^ 2 + 1 g(x) = x/4 g(x) = \mathbb{Z}*x - 1 g(x) = 3x - 1 g(x) = 3x + 1 k(x) = x ^ 2 + x p(x) = - 3/3 - 1