Functions and Graphs

Question 1

N

Answer 1

natural numbers {1,2,3,4,5…}

Question 2

W

Answer 2

whole numbers {0,1,2,3,4…}

Question 3

Z

Answer 3

integers {…-2,-1,0,1,2…}

Question 4

Q

Answer 4

rational numbers eg -4, 1/3, 0.25, -1/3

Question 5

R

Answer 5

real numbers (all points on the number line) eg -6, -1/2, root2, 1/12

Question 6

set

Answer 6

a collection of objects (usually numbers)

Question 7

elements

Answer 7

members of a set

Question 8

subset

Answer 8

a set within a set

Question 9

{}

Answer 9

empty set

Question 10

:

Answer 10

such that

Question 11

function definition

Answer 11

relates a set of inputs to a set of outputs, with each input related to exactly one output.

Question 12

domain

Answer 12

set of inputs

Question 13

range

Answer 13

set of outputs

Question 14

restrictions on the domain

Answer 14

1. denominator cannot equal zero

2. root has to greater than or equal to zero (not negative)

Question 15

composite function

Answer 15

two functions ‘composed’ to form a new ‘composite function’

Question 16

inverse function

Answer 16

reverses the effect of the original function (opposite)

Question 17

inverse function steps

Answer 17

1. replace f(x) with y
2. swap x and y
3. rearrange to y=
4. use notation

Question 18

y=a^x

Answer 18

passes through (0,1) and (1,a)

Question 19

amplitude

Answer 19

half the vertical distance between crest and trough

Question 20

frequency

Answer 20

how many in 360 degrees

Question 21

y=asinbx+c

Answer 21

a=amplitude
b=frequency
c=shift up and down y-axis
d= shift along x-axis

Question 22

steps for naming trig graph

Answer 22

1. check shape (sine/cosine)
2. check amplitude
3. check frequency
4. check shift

Question 23

translation

Answer 23

moves every point on a graph a fixed distance in the same direction. the shape of the graph does not change.

Question 24

y=f(x)+a

Answer 24

moves up or down (up +, down -)

Question 25

y=f(x+a)

Answer 25

moves left or right (left +, right -)

Question 26

y=-f(x)

Answer 26

reflected on x axis

Question 27

y=f(-x)

Answer 27

reflected on y-axis

Question 28

y=kf(x)

Answer 28

stretch or compress in y (stretch when >1, compress when <1)

Question 29

y=f(kx)

Answer 29

stretch or compress in x (stretch when <1, compress when >1)

Question 30

reflection

Answer 30

flips the graph about one of the axes

Question 31

scaling

Answer 31

stretches or compresses the graph along one of the axes