Stccc Prelim Ch 5 Functions

Front 1

Ch 5



What is a function?

Back 1

A function is a relation where for every x-value (in the domain) there is one and only one y-value

Front 2

Ch 5

How to test a graph to determine
if it is a function?

Back 2

Vertical Line test. If a vertical line only cuts the graph once then it is a function

Front 3

Ch 5


If f(x) = x^2 + 2x - 3, then
what does f(a) mean?

Back 3

Replace x with a everywhere
that it appears.
f(a) = a^2 + 2a - 3

Front 4

Back 4

Front 5

Back 5

Front 6

Ch 5 - 6

To sketch a straight line, determine:

Back 6

y-intercept, x = 0
x-intercept, y = 0

Front 7

Back 7

Front 8

Back 8

Front 9

Ch 5 - 8

Back 9

Front 10

Ch 5

Back 10

Front 11

Back 11

Front 12

Back 12

Front 13

Ch 5 - 13

Given the graph of y = f(x) what does y = f(x) + b look like?
What does y - b = f(x) look like?

Back 13

Graph of y = f(x) slides up b units

Front 14

Ch 5 - 14


Given the graph of y = f(x) what does y = f(x - a) look like?

Back 14

Graph of y = f(x) slides to the right by a units

Front 15

Ch 5 - 15


Given the graph of y = f(x) what does y = -f(x) look like?

Back 15

Graph of y = f(x) reflected in x-axis

Front 16

Ch 5 - 16


Given the graph of y = f(x) what does y = f(-x) look like?

Back 16

Graph of y = f(x) reflected in y-axis

Front 17

Ch 5 - 17


Given the graph of y = f(x) what does y =| f(x)| look like?

Back 17

Graph of y = f(x) with sections below x-axis reflected in x-axis

Front 18

Ch 5 - 18



Give definition and description an even function

Back 18

Front 19

Ch 5 - 19



Give definition and description an odd function

Back 19

Front 20

Ch 5 - 20



What is the domain of a function?

Back 20

The domain is all the x values for which the function is defined.

Front 21

Ch 5 - 21



What is the range of a function?

Back 21

The range is all the y values of the function.

Front 22

Ch 5 - 22


Domain and range of
ax + by + c = 0

Back 22

If equation is like 2x + 4y – 3 = 0,
Domain all real x
Range all real y
If equation is like y = 4,
Domain all real x
Range all real y: y = 4

Front 23

Back 23

Domain all real x
Range all real y: y ≥ 0

Front 24

Back 24

Domain all real x
Range all real y

Front 25

Back 25

Domain all real x
Range all real y: y ≥ 0

Front 26

Back 26

Domain all real x
Range all real y: y > 0

Front 27

Back 27

Domain all real x: x ≠ 0
Range all real y: y ≠ 0

Front 28

Back 28

Domain all real x: x ≥ 0
Range all real y: y ≥ 0

Front 29

Back 29

Front 30

Back 30

Front 31

Back 31

Front 32

Back 32

Front 33

Back 33

Domain all real x: (a – r) ≤ x ≤ (a + r)
Range all real y: (b – r) ≤ y ≤ (b + r)

Front 34

Back 34

Semi-circle, above x-axis,
centre (0,0), radius r

Front 35

Back 35

Domain all real x: -r ≤ x ≤ r
Range all real y: 0 ≤ y ≤ r

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Back 36

Front 37

Back 37

Front 38

Back 38

Front 39

Back 39

Front 40

Back 40

Shape
Intercepts
Domain and range
Horizontal asymptotes (x ⇒±∞)
Vertical asymptotes (x undefined)
Plot asymptotes and intercepts
Test positive or negative in regions
Sketch graph

Front 41

Back 41

Front 42

Back 42

Graph the curve with equal sign (dotted if not equal to)
Test either side of line to determine required region
Shade region