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Unit 1 Test Review Which of the following relations are functions? • y=7 • x=7 • x+y=7 Answer • y= 7 is a function – horizontal line will pass the vertical line test. • x =7 is not a function – for the x-value of 7, there are multiple yvalues • x + y =7 is a function - for each value of x, there is a unique value of y The distance D(t) traveled by a jaguar is a function of time (t). • A) Express the following statement using function notation. The jaguar had traveled 150 miles after 3 hours. • B) What does D(1)=50 mean in the context of the problem? • C) What does D(k) = m mean in the context of the problem? Answer • A) D(3) = 150 • B) The jaguar had traveled 50 miles after one hour. • C) The jaguar had traveled m number of miles after k hours. Find 2 possible solutions to the graph of the equation x – 3y + 1 = 4. Answer • Any ordered pair that satisfies the equation is a solution. • Possible answers are (-3, -2), (0, -1), (3, 0), (6, 1)…. Fill in the missing value in the chart. Answer • F(9) = 54 Lauren keeps records of the distances she travels in a taxi and what she pays: a) What is the independent variable? b) What is the dependent variable? c) _____________ is a function of _____________________ d) Write an equation, in function notation, to represent the taxi fare for the distance traveled. e) Interpret the meaning of F(3)=8.25. Answer • a) number of miles • b) taxi fare • c) Taxi fare is a function of distance traveled in miles. • d) F(d) = 2.25d +1.50 • e) Lauren’s taxi fare will cost $8.25 if her destination was 3 miles. How would you recognize a linear function? Answer • Graphically – it’s a line • Numerically – it has a constant rate of change • Symbolically – equation can be rewritten in slope-intercept form How would you recognize a quadratic function? Answer • Graphically – it’s a parabola • Numerically – same y-value for 2 different domain • Symbolically – a variable x is taken to the power of 2 How would you recognize an exponential function? Answer • Graphically – non-linear function that increases or decreases • Numerically – it has a common ratio • Symbolically – the variable x is used as an exponent Your grandma is buying candy bars for Halloween. Assume that there are a total of 80 kids in the neighborhood and each candy bar costs $0.50. • A) What is the domain in the context of the problem? • B) What is the range in the context of the problem? • C) What are some restrictions on the domain and range? Answer • A) Domain is all whole numbers between 0 and 80. • B) Range is $0 to $40, in increments of fifty cents. • C) The values in the domain can’t be decimal, fraction, or negative since we are dealing with number of children. The range has to be 0 or a positive value up to $40 to represent the cost. Since you can’t purchase a fraction of a candy bar, the cost has to increase by fifty cents. For example, your grandma can’t spend $7.25.