Math141HW1B

Math141HW1B - (Exercises for Chapter 1 Functions E.1.1...

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Unformatted text preview: (Exercises for Chapter 1: Functions) E.1.1 CHAPTER 1: Functions (A) means “refer to Part A,” (B) means “refer to Part B,” etc. (Calculator) means “use a calculator.” Otherwise, do not use a calculator. SECTION 1.1: FUNCTIONS #1-2. Finding function rules. Find a function rule of the form f x ( ) = (expression in x ) that is consistent with the input-output machines. (D) 1) 5 ¡ f ¡ ¢ 5 ¡ ¢ £ f £ ¢ ¡ 14.7 ¢ f ¢ 14.7 2) 6 ¡ f ¡ 6 ¡ 3 ¢ f ¢ 3 ¡ 2 3 ¢ f ¢ 2 3 #3-8. Evaluating functions using tables. Fill out the tables. Give exact values unless otherwise specified. (D, F) 3) Let f x ( ) = x + 4 . ( h is a constant or a variable, not a function) Input x Output f x ( ) ¡ 1 0 1 2 5 ¡ 10/3 4.7 c a + h 4) Let f x ( ) = 2 x . ( h is a constant or a variable, not a function) Input x Output f x ( ) ¡ 1 0 1 2 5 ¡ 10/3 4.7 c a + h (Exercises for Chapter 1: Functions) E.1.2 5) Let g t ( ) = t 2 ¡ 9 t + 5 . Input t Output g t ( ) ¡ 2 ¡ 1 0 1 2 c 6) Let h r ( ) = 9 ¡ r 4 . Input r Output h r ( ) ¡ 2 ¡ 1 0 1 2 c 7) Let V r ( ) = 4 3 ¡ r 3 . Input r Output V r ( ) 1 2 5/2 c (If r > , how can V r ( ) be interpreted geometrically?) 8) Let f x ( ) = 7 . Input x Output f x ( ) 1 2 5/2 c (Exercises for Chapter 1: Functions) E.1.3 #9-17. Finding domains. Write the indicated domain in … (G, H) • Task a): … set-builder form (write ¡ when appropriate) • Task b): … graphical form • Task c): … interval form 9) Dom f ( ) , where f x ( ) = 8 x 6 ¡ 3 x 2 + 2 10) Dom f ( ) , where f x ( ) = 1 x ¡ 4 11) Dom g ( ) , where g t ( ) = t 2 + t t + 3 12) Dom g ( ) , where g t ( ) = 7 t 2 t ¡ 1 13) Dom h ( ) , where h r ( ) = r + 2 14) Dom h ( ) , where h r ( ) = r + 2 3 15) Dom h ( ) , where h r ( ) = r + 2 ( ) ¡ 1/2 16) Dom f ( ) , where f x ( ) = 2 ¡ 5 x 4 x + 1 3 17) Dom g ( ) , where g t ( ) = t 4 ¡ 5 3 t 2 ¡ 5 t ¡ 2 (Exercises for Chapter 1: Functions) E.1.4 #18-20. Evaluating functions. (I) 18) Let f x ( ) = x . a) Evaluate f 4 ( ) . b) Evaluate f 11 ( ) . c) Evaluate f a ( ) . d) Evaluate f x + h ( ) . e) Evaluate f x 2 + 2 x + 1 ( ) . 19) Let g t ( ) = 2 t 2 ¡ 3 t ¡ 7 a) Evaluate g 3 ( ) . b) Evaluate g x ( ) . c) Evaluate g t 2 ( ) . d) Evaluate g t + h ( ) . 20) Let h x ( ) = 3 2 x + 1 . a) Evaluate h 5 ( ) . b) Evaluate h ¡ ( ) . c) Evaluate h x + h ( ) . 21) For a function f and some real value a , f a ( ) = a 2 and f a ( ) = 6 a ¡ 9 . Find a . (C, D) (Exercises for Chapter 1: Functions) E.1.5 SECTION 1.2: GRAPHS OF FUNCTIONS 1) Let h r ( ) = 9 ¡ r 4 . Graph p = h r ( ) in the rp-plane by using Point-Plotting and your...
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Math141HW1B - (Exercises for Chapter 1 Functions E.1.1...

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