Math 161 Review for Exam 1 d
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)
(h)
(i)
(l)
(m)
(f)
(g)
(j)
(k)
(n)
Math 161 Review for Exam 1d
page two
2. For each function of problem 1 above give intervals where the function is
(a) increasing
(b) decreasing
(c) constant
3. Given the points  1, 3 and 2, 5
(a) plot the points.
(b) find the midpoint.
(c) find the distance between the points.
4.Plot at least 5 points if possible and sketch the graph
(a) 3, 4, 2, 4, 4, 4
(b) 1, 3, 1, 4
(c) x 2  y 2  25
(e) y  x  5
(f) y  x x
x
(j) y  3  x  1
x 1
(m) y  ( x  2) 2  4 (n) y  2 x  3
(i) y 
2
(q) 2 x  3 y  12
(r) x  5
(g) xy  x  y
(d) x 2 y  y  x
(h) y  2  x  1
3
(k) y  x  2
(l) y  x 3  2
(o) y  3
(s) y  2 x  4
(p) x  1   y  3  25
(t) x 2  y 2  4 x  8 y  11  0
2
2
5. For each part of problem 4 above give the domain, range, and state whether y is a function of
x.
6. For each function of problem 4 above give intervals where the function is
(a) increasing
(b) decreasing
(c) constant
 x 1

2
7. If f  x   2  x  1
 x5

(a) f  3
(f) f  1 2 
(b) f 2
(g) f 1
if x  1
if 1  x  3 sketch the graph and find
if x  3
(c) f 4
(d) f x  2
(h) f x  1 (i) domain of f
(e) difference quotient
(j) range of f
8. Re-do problem 7 above if f  x   x  1  5
9. Re-do problem 7 above if f x   1 x  2
10. The height in feet of a rocket at time t seconds after the fuel runs out is
ht   16t 2  32t  128
(a) Sketch a graph of ht  showing the intercepts and maximum height.
(b) Find the difference quotient.
(c) Find the average velocity of the rocket between 0 seconds and 1 second after fuel runs out.
Math 161 Answers to Review 1d
1.(a) function, domain , range {y: y  2}, x-intercepts (2½,0), (5,0), y-intercept (0,1).
(b) function, domain {x: x  1}, range {y: y  5}, no intercepts.
(c) function, domain {x: x  2}, range {y: y  0}, no x-intercept, y-intercept (0, ½).
(d) function, domain {2, 3, 4}, range {4}, no intercepts.
(e) not a function, domain {1}, range {3, 4}, no intercepts.
(f) not a function, domain {x: 5  x  5}, range {y: 5  y  5},
x-intercepts (5, 0), (5, 0), y-intercepts (0, 5), (0, 5).
(g) function, domain , range {y: ½  y  ½}, x-intercept (0, 0), y-intercept (0, 0).
(h) not function,domain {x: x  5}, range , x-intercept (5, 0), y-intercepts (0, 5),(0,5).
(i) function, domain {x: x  0}, range {1, 1}, no intercepts.
(j) function, domain {x: x  1}, range {y: y  1}, x-intercept (0, 0), y-intercept (0, 0).
(k) function, domain , range , x-intercept (¼, 0), y-intercept (0, 1).
(l) function, domain , range {y: y  4}, x-intercepts (4,0), (0,0), y-intercept (0,0).
(m) function, domain , range {y: y  3}, x-intercepts (2,0), (4,0), y-intercept (0,2).
(n) function, domain , range set of integers, x-intercepts {x: 0  x < 1}, y-intercept (0,0).
2.(a) increasing on 0,1  3,  , decreasing on  , 0  1, 3 .
(b) increasing on 1,  .
(c) decreasing on  , 2  2,  .
(d) function is not defined on intervals.
(e), (f) not a function.
(g) increasing on  1,1 , decreasing on  ,  1  1,  .
(h) not a function.
(i) constant on  , 0  0,  .
(j) decreasing on  ,1  1, 
(k) increasing everywhere.
(l) increasing on 0,  , decreasing on  , 0 .
(m) increasing on  ,1 , decreasing on 1,  .
(n) constant on intervals of the form n, n  1 where n is an integer.
3.(a)
3.(b)
10.(a)
12 , 4 .
(c) 13 .
10. (b)  32t  32  16h
(c) 16 feet per second.
Math 161 Answers to Review 1d
4. (a)
page two
(b)
(e)
(c)
(f)
(d)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
Math 161Answers to Review 1d
page three
(o)
(p)
(q)
(r)
(s)
(t)
5. domain (a) {2, 3, 4} (b) {1}
range
{4}
{3,4}
function?
yes
no
(c) {x:  5  x  5}
{y:  5  y 5}
no
(d) all real numbers
{y:  ½  y  ½ }
yes
(e) {x: x   5}
all real numbers
no
(f) {x: x  0}
{1, 1}
yes
(g) {x: x  1}
{y: y  1}
yes
(i) all real numbers
y :  12  y  12
yes
(j) all real numbers
y : y  3
yes
(k) x : x  2
y : y  0
yes
(l) all real numbers
all real numbers
yes
(m) all real numbers
y : y  4
yes
(n) all real numbers
all real numbers
yes
(o) all real numbers
3
yes
(p) x : 4  x  6
y : 2  y  8
no
(q) all real numbers
all real numbers
yes
(h) all real numbers
all real numbers
yes
Math 161 Answers to Review 1d
(r) 5
all real numbers
no
page four
(t) x : 1  x  5
y : 7  y  1
no
(s) all real numbers
all real numbers
yes
6.(a) function not defined on intervals.
(b) not a function.
(c) not a function.
(d) increasing on  1,1 , decreasing on  ,  1  1,  .
(e) not a function.
(f) constant on  , 0  0,  .
(g) decreasing on  ,1  1,  .
(h) increasing everywhere.
(i) increasing on  1,1 , decreasing on  ,  1  1,  .
(j) increasing on  ,1 , decreasing on 1,  .
(k) increasing on 2,  .
(l) increasing everywhere.
(m) increasing on  2,  , decreasing on  ,  2 .
(n) increasing everywhere
(o) constant everywhere.
(p),(r),(t) not a function.
(q),(s) increasing everywhere.
7. (a) 4
(b) 1
 x  2 1

2
(d) 2   x  1
 x3

(c)  1
(i) all real numbers
(j) {y: y   2}
1
if x  0

 x 1 1
if x  1
if x  2

1
if 0  x  1


2
if  1  x  1 (e) 
(h) 2   x  2  if 2  x  4
 2 x  2  h if 1  x  3
 x6

if x  1
if x  4


1
if x  3
8. (a) undefined (b) 6
(f) undefined
9.(a)  1 5
(f)  2 3
7.
(g) 5
(f)
3
2
(g) 2
x  1  5 (e) 1

(c)
3 5
(h)
x  2  5 (i) {x: x  1} (j) {y: y  5}
(d)
(b) undefined (c) 1 2
(g)  1
(h) 1 x  3
(d) 1 x
(i) {x: x  2}
8.
x  h 1  x 1

(e)  1 x  2  hx  2
(j) {y: y  0}
9.