Week_5_M1508_Worksheet#1_Solutions.pdf - Week 5 Math 1508...

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Unformatted text preview: Week 5 Math 1508 Worksheet – Review of first 5 weeks 1. Find the x- and y-intercepts for the following functions a. = |4 − 12| (3,0) b. = 2 3 − 8 (−2,0), (0,0), (2,0) 2. Find the equation of the line passing though the given points. a. (−3, −3) ; (4, −3) = −3 3 3 1 b. (1, ) ; (− , ) 4 4 2 1 17 = + 7 28 3. Write the equation of the lines through the given point (a) parallel to and (b) perpendicular to the given line. a. 4 − 2 = 3, (5, −2) 1 1 : = 2 − 12, : = − + 2 2 3 2 b. 5 + 3 = 3, ( , − ) 4 5 5 17 3 17 : = − + , : = − 3 20 5 20 4. Evaluate the function at each specified value of the independent variable and simplify. 4 − 8 ≤ −3 a. () = { 5 −3 < < 2 5 5− ≥2 i. (−3) (−3) = 28 ii. (0) (−3) = 5 5 iii. ( ) 2 5 2965 ( ) = − 2 32 b. () = − 2 − 6 + 4 i. (−2) (−2) = 12 2 ii. ( ) 3 2 4 ( ) = − 3 9 5. Find the inverse for the given functions, then state the domains and ranges for and −1 . a. () = 9+2 5−2 −1 () = −2 − 9 2 − 5 Domain 2 2 (−∞, ) ∪ ( , ∞) 5 5 2 2 (−∞, ) ∪ ( , ∞) 5 5 () −1 () b. () = √ 2 + 6, Range 2 2 (−∞, ) ∪ ( , ∞) 5 5 2 2 (−∞, ) ∪ ( , ∞) 5 5 ≥0 () −1 () = √ 2 − 6 Domain (−∞, ∞) −1 () [√6, ∞) Range [√6, ∞) (−∞, ∞) Identify the vertex, axis of symmetry, and x- and y-intercepts for the following function. () = 2 2 + 12 + 2 : = −3 : (−3, −16) − : (0,2), − : (−3 − 2√2, 0) ((−3 + 2√2, 0) ) 6. Explain in your own words how the Intermediate Value Theorem helps you find real zeros of a polynomial function. “The Intermediate Value Theorem helps you locate the real zeros of a polynomial function in the following way. If you can find a value x=a at which a polynomial function is positive, and another value x=b at which it is negative, then you can conclude that the function has at least one real zero between thee tow values” (Larson, 2014, p. 131). [Answers may vary] 7. Find the real zeros for the following polynomial functions a. () = 3 3 − 19 2 + 33 − 9 1 (3,0), (3,0)[ ], ( , 0) 3 b. () = 3 4 − 8 3 − 37 2 + 2 + 40 4 (−2,0), (− , 0) , (1,0) (5,0) 3 8. Write the polynomial as the product of linear factors and list all the zeros of the function. () = 3 + 8 + 11 − 20 ( + 5)( − 1)( + 4) 9. Use the given zero to find all the zeros of the function a. () = 4 + 3 3 − 5 2 − 21 + 22 −3 + √2 = −3 + √2 , = −3 − √2 , = 1, = 2 b. () = 3 + 4 2 + 14 + 20 −1 − 3 = −1 − 3, = −1 + 3, = −2 ...
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