Chapter 1 Functions and Models

Question 1

What is a function?

Answer 1

A funciton f is a rule that assigns to each element x in a set D exactly one element called f(x), in a set E.

Question 2

Domain

Answer 2

All elements of x or all the possible inputs

Question 3

Range

Answer 3

All elements of y or all the possible outputs

Question 4

Independent Variable

Answer 4

Arbitrary number in the domain of a function

Question 5

Dependent Variable

Answer 5

A symbol that represents a number in the range of the function

Question 6

What are the four different ways to represent a function?

Answer 6

Verbally
Numerically
Visually
Algebraically

Question 7

y = f(x) + c does what?

Answer 7

shifts the graph f(x) a distance of C units upwards

Question 8

y = f(x) -c does what?

Answer 8

shifts the graph f(x) a distance of C units downward

Question 9

y = f(x+c) does what?

Answer 9

shifts the graph f(x) a distance of C units to the left

Question 10

y = f(x-c) does what?

Answer 10

shifts the graph f(x) a distance of C units to the right

Question 11

y = c f(x) does what?

Answer 11

stretches the graph vertically by a factor of C

Question 12

y = (1/c) f(x) does what?

Answer 12

shrink the graph vertically by a factor of C

Question 13

y = f(cx) does what?

Answer 13

shrink the graph horizontally by a factor of C

Question 14

y = f(x/c) does what?

Answer 14

stretch the graph horizontally by a factor of C

Question 15

y = -f(x) does what?

Answer 15

reflect the graph across the x-axis

Question 16

y = f(-x) does what?

Answer 16

reflect the graph across the y-axis

Question 17

b^x+y =

Answer 17

b^x * b^y

Question 18

b^x-y =

Answer 18

b^x / b^y

Question 19

(b^x)y

Answer 19

b^xy

Question 20

(ab)^x

Answer 20

a^x * b^x

Question 21

f(x) is one-to-one when?

Answer 21

it never takes on the same value twice

Question 22

what is an inverse function?

Answer 22

f^-1 (y) = x
f(x) = y

Question 23

log b (xy) =

Answer 23

log b x + log b y

Question 24

log b (x/y)

Answer 24

log b x - log b y

Question 25

log b (x)^r

Answer 25

r log b (x)

Question 26

ln x =

Answer 26

log e (x)

Question 27

e ^ ln (x) =

Answer 27

x

Question 28

x^r =

Answer 28

e^ r ln x

Question 29

change of base formula

Answer 29

log b x = ln x / ln b