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1 Math 131 WIR, copyright Angie Allen Math 131 Week-in-Review #1 (Sections 1.1 and 1.2) 1. Classify each of the following as a power function, root function, rational function, polynomial function (state its degree), algebraic function, trigonometric function, exponential function, or logarithmic function. a) f (x) = 2x c) √ x + x9 b) h(x) = 1 − x2 d) g(x) = 1 x 2. At 8am, rain begins to fill an empty bird bath. By 10am, the bird bath is full of water, and it stops raining at 11am. At 2pm, Jerry, a blue bird, takes a dip in the bath. After 30 minutes, Jerry leaves the bath. a) Sketch a rough graph of the volume of water in the bird bath as a function of time. Assume Jerry does not take any water with him when he leaves the bath! b) Would your graph change if you were to sketch the height of the water in the bird bath as a function of time? 2 Math 131 WIR, copyright Angie Allen 3. A cell phone company has a base charge of $20/month. The first 100 minutes are free, and the next 400 minutes cost $0.10/minute. Any usage over 500 minutes costs $0.15/minute. Find a function, C(x), which gives the amount of a cell phone bill during a month when a customer uses x cell phone minutes. 4. Rewrite the function k(t) = t 2 + |t − 6| √ as a piecewise function and find its domain. 3 t +5 5. Determine whether the functions f (x) = x2 |x| + 2 and g(x) = x3 |x| + 2 are even, odd, or neither. Math 131 WIR, copyright Angie Allen 3 6. Find the domain of the following functions. √ 4 2x2 − 9x − 18 . a) h(x) = 2x−3 b) g(x) = √ √ x+ 6−x . 4x2 − 16 7. A rectangle is inscribed inside a circle with radius 4. Express the area of the rectangle as a function of its width, w, and find its domain. 4 Math 131 WIR, copyright Angie Allen 8. The per capita consumption of apple juice in Appleville has increased in the past 10 years as shown in the table. Year Liters per person per year 2000 1.8 2002 1.9 2004 2.2 2006 2.6 2008 3.2 2010 3.9 a) Find an appropriate model to fit the data. b) Use your unrounded model to estimate the per capita consumption in 2012. c) According to the unrounded model, when will per capita apple juice consumption exceed 8 liters per person per year? 5 Math 131 WIR, copyright Angie Allen 9. 1 41 cups of pancake mix will make 2 12 7-inch pancakes. 3 43 cups of mix will make 7 21 7-inch pancakes. a) Find a formula for the number of 7-inch pancakes, p, as a function of the amount of mix used, m, assuming the relationship is linear. b) Interpret the slope of this function. c) If Uncle Buck needs to make 63 7-inch pancakes for a birthday party, how many cups of mix does he need? Round to the nearest cup, i.e., integer. 10. Find a formula for the function f shown below. 4 y 3 2 1 −4 −3 −2 −1 1 −1 −2 −3 −4 2 3 4 x 6 Math 131 WIR, copyright Angie Allen 11. If the point (a − j, s) is on the graph of an even function, what other point must also be on the graph of the function? 12. Evaluate the difference quotient x+2 f (a + h) − f (a) for the function f (x) = and simplify your answer. h x−3 13. A function f has domain [−7, 7] and part of the graph is shown below. Complete the graph if it is known that f is odd. final answer: scratch work: y y x −7 7 x −7 7 7 Math 131 WIR, copyright Angie Allen 14. Graph the following piecewise-defined function AND find its domain. 2 x − 2 −5 ≤ x < 1 f (x) = 4 x=3 3x − 1 x>3 y x 15. Find the domain of the following function: 3x + 4x −5 < x ≤ −1 x √ −1 < x < 1 f (x) = x−1 x−3 x>1 x2 − 9