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Answers to Review Exam 3 - Precalculus I | MATH 161, Exams of Pre-Calculus

Community College of Philadelphia Pre-Calculus

Material Type: Exam; Class: Precalculus I; Subject: Mathematics; University: Community College of Philadelphia; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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Math 161 Review for Exam 3

In all graphs shown assume that if a curve or pattern goes to the edge of the displayed coordinate

system that the curve or pattern continues indefinitely in that direction.

1. For each graph state whether y is a function of x and estimate domain, range, x-intercepts, and

y-intercepts.

(a) (b) (c)

(d) (e) (f) (g)

(h) (i) (j) (k)

(l) (m) (n)

Partial preview of the text

Download Answers to Review Exam 3 - Precalculus I | MATH 161 and more Exams Pre-Calculus in PDF only on Docsity!

Math 161 Review for Exam 3 In all graphs shown assume that if a curve or pattern goes to the edge of the displayed coordinate system that the curve or pattern continues indefinitely in that direction.

For each graph state whether y is a function of x and estimate domain, range, x-intercepts, and y-intercepts. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n)

Math 161 Review for Exam 3 page two

Write the equation for each graph in problem 1 that is a rigid transformation of a common function.
Use Graph 3 above to estimate:

(a) domain (b) range (c) zeros (d) relative extremes (e) symmetry (f) f^ ^ ^2  (g) f ^1 

intervals where the function is (h) increasing (i) decreasing (j) constant (k) positive

and sketch the graphs of (l) f^ ^ x ^ ^2 (m) f^ ^ x ^ ^3 (n) f^ ^ x ^1  (o) ^ f ^ x  (p) 2 f ^ x 

4. Use Graph 4 above to sketch the graph of (a) ^ f^ ^ g ^ x  (b) ^ f^ ^ g ^ x  (c) ^ g^  f ^ x 

Let ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ , ^ ^23 , 1 1 , 2 1 2 , 2 , 1 ,             kx x x j x x f x x gx x hx x i x

l x  x   mx  x  , ^ ^

           4 2 2 2 x^2 if x x if x n x.

(a) Find f^ ^2.^3 , f^ ^ ^1.^4 , g^ ^6 , h ^^ ^4 , i ^^1 , j ^^ ^1 , k^ ^4 , l^ ^5 , m^ ^ ^2 , n ^ ^1 

(b) Find ^ f^ ^ g ^ x , ^ l^ ^ m ^ x , ^ km ^ ^ x , ^ hj^ ^ x , ^ kn^ ^ x , ^ i^ j ^ x and their domains.

(c) Find ^ i^ ^ j ^ x , ^ l^ ^ k ^ x , ^ n^ ^ h ^ x and their domains.

(d) Find functions o ^^ x  and p ^^ x  such that l^ ^ x ^ ^ o  p ^ x .

For each function: (e) Sketch the graph. (f) Find the domain and range. (g) Find the zeros, x-intercepts and y-intercepts. (h) Find the relative extremes. (i) Find the intervals where the function is increasing, decreasing, constant, and positive. (j) Describe the function in terms of shifts, reflections, stretching, or shrinking of the

common functions x^ ,^ x^2 , x^3 ,^1 x , x , x ,^ ^ x . Be as specific as possible.

Around the turn of the century the rate for first class mail in the U.S. was 33 cents for up to an ounce and an additional 22 cents for each additional ounce or fraction of an ounce. (a) Express postage as a function of number of ounces using greatest integer function. (b) Draw a graph of the function.

Math 161 Review 3 Answers page two

(a) (b) (c) 5.(a) 4,0,2,3,1,undefined, 5,0,7,

(b)  f  g  x    x   2  x  2 , domain {x: x  2}

 l  m  x   x^3  x^2  6 x  4 , domain 

 km  x   2 x^4  3 x^3  2 x  3 , domain 

            1 1 1 1 1 1 if x if x x x hj x. domain {x: x  1}

               2 3 8 12 2 2 6 2 3 2 2 x x x if x x x if x kn x , domain 

2 1    x x i j x , domain {x: x  1 and x  2}

(c) ^ ^ ^

2 1 1     x x i  j x , domain {x: x  ½ and x  1}

 l  k  x   4  x  3  2  4 , domain .,  n  h  x   4  x  1  2 , domain .

(d) ^ ^4

o x  x^2 

, p ^ x ^  x ^3

(f) f(x) domain , range integers g(x) domain {x: x  2}, range {y: y  0} h(x) domain , range {y: y  0} i(x) domain {x: x 2}, range {y: y  0} j(x) domain {x: x 1}, range {y: y  0} k(x) domain , range  l(x) domain , range {y: y   4} m(x) domain , range  n(x) domain , range  (g) f(x) zeros {x:  2  x <1}, x-intercepts {(x,0):  2  x <1}, y-intercept (0, 2). g(x) zero 2, x-intercept (2, 0), no y-intercept. h(x) zero 1, x-intercept (1, 0), y-intercept (0, 1). i(x) no zero,no x-intercept,y-intercept(0, ½). j(x) no zero,no x-intercept, y-intercept (0, 1).

k(x) zero 3 2 , x-intercept ^3 2 ,^0 , y-intercept (0, 3).

l(x) zeros 1, 5, x-intercepts (1, 0), (5, 0), y-intercept (0, 5). m(x) zeros 1, x-intercept (1, 0), y-intercept (0, 1). n(x) zeros 2, 2, x-intercepts (2, 0), (2, 0), y-intercept (0,4). Math 161 Review 3 Answers page three (e) f(x) g(x) h(x)

i(x) j(x) k(x) l(x) m(x) n(x) (h) f(x) every number is both a relative minimum and a relative maximum except the integers. i(x), j(x), k(x), m(x) no relative extremes. g(x) relative minimum 0 when x = 2, no relative maximum. h(x) relative minimum 0 when x = 1, no relative maximum. l(x) relative minimum  4 when x = 3, no relative maximum. n(x) relative minimum 0 when x = 2, relative maximum 4 when x = 0.