Pianos as Functions

Pianos as Functions

Draw

Plug in 0, 1, and 2 in for $$x$$ and list the values:

function = $$50\left(2\right)^x$$

Learning Goal

SWBAT:

• Describe the domain and range of a function

• Evaluate a function at a given input value

​What happens when you play a piano?

Word Cloud

What are the inputs on this piano?

​What inputs did you see?

Talk with your shoulder partner

Each key (input) has it's own frequency (output)!

The frequency of a note tells you how high or low a sound is.

​The higher the frequency, the higher the sound.
The lower the frequency, the lower the sound.

​Write the frequency that each key gives you.

What are the outputs?

Drag and Drop

The keys on a piano are

Placeholder

, the frequencies or sounds that come out are ​

Placeholder

.

Drag these tiles and drop them in the correct blank above

inputs

outputs

cats

Pianos = Functions

x

Inputs (Domain):

key

Inputs (Domain):

Outputs (Range):

piano(key) = frequency

Outputs (Range):

function(x) = y

What pattern do the A-keys make?

​Talk to your face partner!

Multiple Choice

$$piano\left(A_4\right)=?$$

• 220

• 3000

• 3520

• 5

Multiple Choice

If $$f\left(x\right)=220\left(2\right)^x$$ , then $$f\left(4\right)=?$$

• 220

• 3000

• 3520

• 5

Multiple Choice

If $$f\left(x\right)=220\left(2\right)^x$$ , then $$f\left(5\right)=?$$

• 400

• 7040

• 3000

• 5

Multiple Choice

If you inputed a key on the piano, and the frequency 392 was outputed, what key did you play?

• A

• G

• F

• C

​Talk with your shoulder partner!

Will playing the low-C ever give me a different frequency?

https://www.intmath.com/trigonometric-graphs/music-note-frequencies-interactive.php

Open Ended

On the piano screen play the frequencies in order:

261.63, 261.63, 392, 392, 440, 440, 392

What keys did you play? What song is that?

Poll

Does this table represent a function?

• Yes

• No

• Sometimes

Talk with your shoulder partner about your choice!

Drag and Drop

In a function, every​

Placeholder

has exactly one​

Placeholder

.

Drag these tiles and drop them in the correct blank above

input

output

cat

Multiple Choice

$$f\left(4\right)=?$$

• 10

• 12

• 31

• 32

Multiple Choice

$$f\left(-3\right)=?$$

• 10

• 12

• 31

• 32

Multiple Choice

Does this table represent a function?

• Yes

• No

Multiple Choice

If $$f\left(x\right)=2x+1$$ , then $$f\left(2\right)=?$$

• 1

• 2

• 5

• 20

Multiple Choice

If $$f\left(x\right)=2x+1$$ , then $$f\left(3\right)=?$$

• 7

• -1

• 3

• 200

Multiple Choice

Evaluate: $$y=2\left(10\right)^x$$  when x = 0

• 2

• 0

• 1

• 20

Multiple Choice

f(x)=4x+5
f(4)=

• 21
• -11
• -31
• 25

Multiple Choice

f(x)=x+3
f(x) = -5

• -2
• -1
• -8
• 7

Multiple Choice

Evaluate: $$y=6^x$$  when x = 1

• 1

• 6

• 0

• $$\frac{1}{6}$$  

Multiple Choice

g(x) = 5 - 6x
Find g(-5)

• g(-5) = -25
• g(-5) = 6
• g(-5) = 4
• g(-5) = 35

Multiple Choice

g(x) = 11 - x
Find g(x) = -7 

• 4
• 17
• 18
• -77

Multiple Choice

Evaluate f(-5) if f(x) = -2x - 12

• -22
• -2
• -19
• -5

Multiple Choice

Evaluate y = x + 5 when y = 10.

• 8
• 2
• 9
• 5

Multiple Choice

What is f(2)?

• -4
• 8
• 0
• 5