Math 161 Review for Exam 3d
1. Solve for x.
(a) 2 x 2  3  5 x
(e) x 2  4  0
(b) 3x 2  5  7 x
(f) x 2  5 x  6
(c) 2 x 2  7 x  6
(g) x 2  4 x  3
(d) x 2  6  0
(h) x 2  9  6 x
2. Solve for x and check your answer by replacing x with your answer in the original equation.
x 2  8 x  20  0
3. Solve for x and sketch the graph on the number line.
2x  5
 5 (b) 2 x  7  1 (c) x 2  4 x  5
(a)  4 
3
(d) 5 x 2  x 2  6
(e) x  3  5
4. Find a formula for the quadratic function satisfying:
(a) vertex (3, 2), point (1, 6)
(b) vertex (1, 2), intercept (0, 3)
5. Identify the vertex and intercepts and graph the following quadratic functions.
(a) f x   x 2  4 x  9
(b) f x   9  x 2
(c) f x   x 2  6 x  15
6. Use the graph of the function y = f(x) to draw the graph of its inverse if possible.
(a)
(b)
(c)
7. Find the inverse function and its domain if possible.
(a) {(2, 4), (3, 5), (3, 7)}
(b) 1, 9, 2, 6, 3, 4
8. Find the inverse function and its domain if possible.
1
(a) f x  
(b) f  x   x
x2
(d) f x   x 2
(e) f x   x x
(g) f x   x
(h) f x   x 3  1
(c) cx  5x  32 / 9
 x if x  0
(f) f x    2
 x if x  0
(i) f x   x 3  3x 2
Math 161 Answers to Review for Exam 3d
1.(a) x 
3
2
7  11 i
7  97
(c) x 
6
4
(g) x : x  2  7 or x  2  7
(d)  (e) x : 2  x  2
(b) x 
or 1
(f) x : 1  x  6


(h) x  3
2. Answer x   4  2 i
x 2  8 x  20  0
Check x   4  2 i :
 16  8 i  8 i  4 i 2  32  16 i  20  0 ?
 16  4  32  20  0 ?
x 2  8 x  20  0
Check x   4  2 i :
 16  8 i  8 i  4 i 2  32  16 i  20  0 ?
 16  4  32  20  0 ?
3
2
2
 16  4 i 2  32  20  0 ?
 0  0 ? Yes.
2
  4  2 i   8 4  2 i   20  0 ?
 16  4 i 2  32  20  0 ?
 0  0 ? Yes.
(b) 3  x  4
3.(a)  3 1 2  x  10
(d)  1.2  
  4  2 i   8 4  2 i   20  0 ?
x
4.(a) f  x    x  3  2
2
5.(a) vertex (2, 5),
intercept (0, 9).
3
2
(c)  5  x  1
 1.2 (e) x  2 or x  8
(b) f x   x  1  2
2
(b) vertex (0, 9),
intercepts (0, 9), ( 3, 0).
(c) vertex (3, 24),
intercepts (0, 15), 3  2 6 ,0


Math 161 Review 3d Answers
6.(a)
(b)
7.(a) not a function
(b) inverse {(9, 1), (6, 2), (4, 3)}, domain {9, 6, 4}
x   2  1 x , domain {x: x  0}
(c) c 1 x   9 5 x  32 , domain 
8.(a) f
(e) f
1
1

 x   
(c) no inverse
x
if x  0
, domain 
if x  0
 x
(g) no inverse (h) f 1 x   3 x  1 , domain 
(b) f 1 x   x 2 , domain {x: x  0}
(d) no inverse
(f) f
1
x
if x  0
 x
if x  0
x   
(i) no inverse
, domain 