Math Journal 9-11Find the value of the function when the input is

1. 2. 3.

Unit 2 Day 5: Comparing Functions

Essential Questions: How do linear, exponential, absolute value, and square root

functions differ from each other? What causes a shift in a graph?

Vocabulary• Linear: a straight line with a constant rate of

change.

• Exponential: a function whose rate of change increases/decreases over time.

• Square Root: a number that produces a specific quantity when multiplied by itself.

Ex:

• Intercepts (x & y): the points where the graph of a function crosses the x and / or y axis.

General Rule For Graphing

This rule always works: when in doubt make a table and plot it out!

x y = 2x y

-2 y = 2(-2) -4

-1 y = 2(-1) -2

0 y = 2(0) 0

1 y = 2(1) 2

2 y = 2(2) 4

Plug whatever x-values you want into the given

function.

Make it easy on yourself by

choosing easy numbers!

Linear Functions• f(x) = 10x

• This function can represent getting paid 10 dollars per hour.

• The variable (x) represents hours. Notice how it has a constant rate of change of $10 for every 1 hour.

10

20

30

40

50

1 2 3 4 5

Linear Functions: Shifts

• f(x) = 10x + 15

• This function can represent getting paid 10 dollars per hour.

• The variable (x) represents hours. What could the “+15” stand for?

10

20

30

40

50

1 2 3 4 5

Linear Functions: Shifts

• f(x) = 10x - 20

• This function can represent getting paid 10 dollars per hour.

• The variable (x) represents hours. What could the “- 20” stand for?

10

20

30

40

50

1 2 3 4 5

Example 1: Match the function to its graph.

f(x) = x - 2

f(x) = x + 2

f(x) = x

f(x) = x - 5

Example 1: Match the function to its graph.

f(x) = x - 2

f(x) = x + 2

f(x) = x

f(x) = x - 5

Exponential Functions

Why do you think these graphs are growing at

a different rate?

Why do they all have the

same y-intercept?

(-1, 1/2 ) (-1, 1/3) (-1, 1/10)

(0,1 ) (0,1) (0,1)

(1,2) (1, 3) (1,10)

(2,4) (2, 9) (2, 100)

(3,8) (3, 27) (3, 1000)

Absolute Value Functions• An absolute value graph always has a

“V” shape.

• f(x) = |x|

• f(x) = -|x|X

y = -|x| y

-2y = -|-

2|- 2

-1y = -|-

1|- 1

0y = -|

0| 0

1y = -|

1|- 1

2y = -|

2|- 2

X y = |x| y

-2y = |-

2| 2

-1y = |-

1| 1

0 y = |0| 0

1 y = |1| 1

2 y = |2| 2

Square Root Functions• Square root functions

are curved and usually level off as ‘x’ gets bigger.

• Why do you think it levels off?

• Why isn’t the negative part of the graph being used?

Square Root Functions: ShiftsSquare root functions shift the same as other functions:

• Subtracting a number causes a shift down• Adding a number causes a shift up

Example 2: Matchingf(x) = xf(x) = 2x f(x) = |x| f(x) = ✓x

Example 2: Matching

f(x) = x

f(x) = 2xf(x) = |x|

f(x) = ✓x

-5

f(x) = x + 2

f(x) = 2x - 3

f(x) = |x| - 3

Example 3: Matching

𝑓 (𝑥 )=√𝑥+3

-5

f(x) = x + 2

f(x) = 2x - 3

f(x) = |x| - 3

Example 3: Matching

𝑓 (𝑥 )=√𝑥+3

Test Your Skills!

• http://www.regentsprep.org/Regents/math/algtrig/ATP5/FuncPrac.htm

SummaryEssential Questions: How do linear, exponential, absolute value, and square root functions differ from each other? What causes a shift in a graph?

Take 1 minute to write 2 sentences answering the essential questions.