Question

Find a Sinusoidal Function for Each of the Graphs Above ​

Answer 1

Answer:

• ꜱᴏʟᴜᴛɪᴏɴ :

ᴛʜᴇ ꜱᴄᴀʟɪɴɢ ᴀʟᴏɴɢ ᴛʜᴇ ʏ-ᴀxɪꜱ ɪꜱ ᴏɴᴇ ᴜɴɪᴛ ꜰᴏʀ ᴏɴᴇ ʟᴀʀɢᴇ ᴅɪᴠɪꜱɪᴏɴ ᴀɴᴅ ᴛʜᴇʀᴇꜰᴏʀᴇ ᴛʜᴇ ᴍᴀxɪᴍᴜᴍ ᴠᴀʟᴜᴇ ᴏꜰ ʏ: ʏᴍᴀx = 1 ᴀɴᴅ ᴛʜᴇ ᴍɪɴɪᴍᴜᴍ ᴠᴀʟᴜᴇ ᴏꜰ ʏ: ʏᴍɪɴ = - 7. ᴛʜᴇ ꜱᴄᴀʟɪɴɢ ᴀʟᴏɴɢ ᴛʜᴇ x ᴀxɪꜱ ɪꜱ π ꜰᴏʀ ᴏɴᴇ ʟᴀʀɢᴇ ᴅɪᴠɪꜱɪᴏɴ ᴀɴᴅ π/5 ꜰᴏʀ ᴏɴᴇ ꜱᴍᴀʟʟ ᴅɪᴠɪꜱɪᴏɴ.

ᴘᴏɪɴᴛꜱ ᴀ ᴀɴᴅ ʙ ᴍᴀʀᴋ ᴛʜᴇ ꜱᴛᴀʀᴛ ᴀɴᴅ ᴛʜᴇ ᴇɴᴅ ᴏꜰ ᴏɴᴇ ᴘᴇʀɪᴏᴅ ᴘ ᴡʜɪᴄʜ ɪꜱ ᴇQᴜᴀʟ ᴛᴏ 5π. ᴛʜᴇꜱᴇ ᴘᴏɪɴᴛꜱ ᴀʀᴇ ᴜꜱᴇꜰᴜʟ ʙᴇᴄᴀᴜꜱᴇ ᴛʜᴇʏ ᴀʀᴇ ᴍᴀxɪᴍᴜᴍ ᴘᴏɪɴᴛꜱ ᴡɪᴛʜ ᴄʟᴇᴀʀ ᴄᴏᴏʀᴅɪɴᴀᴛᴇꜱ.

ꜱɪɴᴄᴇ ᴀ ᴀɴᴅ ʙ ᴀʀᴇ ᴍᴀxɪᴍᴜᴍ ᴘᴏɪɴᴛꜱ, ɪᴛ ɪꜱ ᴇᴀꜱɪᴇʀ ᴛᴏ ᴡʀɪᴛᴇ ᴀɴ ᴇQᴜᴀᴛɪᴏɴ ꜰᴏʀ ᴛʜᴇ ɢʀᴀᴘʜ ᴀꜱ ʏ = ᴀ ᴄᴏꜱ[ ʙ(x - ᴅ) ] + ᴄ ᴀꜱꜱᴜᴍɪɴɢ ᴛʜᴀᴛ ᴏʀɪɢɪɴᴀʟʟʏ ɪᴛ ɪꜱ ᴀ ᴄᴏꜱ(x), ᴡʜɪᴄʜ ꜱᴛᴀʀᴛꜱ ᴡɪᴛʜ ᴀ ᴍᴀxɪᴍᴜᴍ ᴀᴛ x = 0, ᴛʜᴀᴛ ɪꜱ ᴛʀᴀɴꜱꜰᴏʀᴍᴇᴅ ʙʏ ᴠᴇʀᴛɪᴄᴀʟ ᴀɴᴅ ʜᴏʀɪᴢᴏɴᴛᴀʟ ꜱʜɪꜰᴛɪɴɢ (ᴛʀᴀɴꜱʟᴀᴛɪᴏɴ) ᴀɴᴅ ᴠᴇʀᴛɪᴄᴀʟ ᴀɴᴅ ʜᴏʀɪᴢᴏɴᴛᴀʟ ꜱᴛʀᴇᴛᴄʜɪɴɢ/ꜱʜʀɪɴɢᴋɪɴɢ.

• ʟᴇᴛ ᴜꜱ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴀ, ᴀɴᴅ ᴄ.

|ᴀ| = (ʏᴍᴀx - ʏᴍɪɴ) = (1 - (-7)) / 2 = 4. ᴡʜɪᴄʜ ɢɪᴠᴇꜱ ᴛᴡᴏ ᴘᴏꜱꜱɪʙʟᴇ ᴠᴀʟᴜᴇꜱ ꜰᴏʀ ᴀ:ᴀ = 4 ᴏʀ ᴀ = - 4

ᴛʜᴇ ɢʀᴀᴘʜ ʙᴇᴛᴡᴇᴇɴ ᴀ ᴀɴᴅ ʙ ʜᴀꜱ ɴᴏ ʀᴇꜰʟᴇᴄᴛɪᴏɴ ᴡʜᴇɴ ᴄᴏᴍᴘᴀʀᴇᴅ ᴛᴏ ᴛʜᴇ ᴘᴇʀɪᴏᴅ ᴏꜰ ᴄᴏꜱ(x) ʙᴇᴛᴡᴇᴇɴ 0 ᴀɴᴅ 2π ᴀɴᴅ ᴡᴇ ᴍᴀʏ ᴛʜᴇʀᴇꜰᴏʀᴇ ᴛᴀᴋᴇ ᴀ = 4.

ᴄ = (ʏᴍᴀx + ʏᴍɪɴ) = (1 + (-7)) / 2 = - 3

• ᴘᴇʀɪᴏᴅ: ᴘ = 2π|ʙ|= 5π

ꜱᴏʟᴠᴇ ᴛʜᴇ ᴀʙᴏᴠᴇ ꜰᴏʀ |ʙ| ᴛᴏ ᴏʙᴛᴀɪɴ: |ʙ| = 2/5.

ᴀɢᴀɪɴ ʜᴇʀᴇ ᴡᴇ ʜᴀᴠᴇ ᴛᴡᴏ ᴘᴏꜱꜱɪʙʟᴇ ᴠᴀʟᴜᴇꜱ ꜰᴏʀ ʙ: ʙ = 2/5 ᴀɴᴅ ʙ = -2/5. ᴡᴇ ᴛᴀᴋᴇ ʙ = 2/5 ᴛᴏ ᴍᴀᴋᴇ ᴏᴜʀ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ ꜰᴏʀ ᴅ ᴇᴀꜱɪᴇʀ.

ᴡᴇ ɴᴏᴡ ᴡʀɪᴛᴇ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ꜰᴏʀ ᴛʜᴇ ɢʀᴀᴘʜ ᴀꜱ ꜰᴏʟʟᴏᴡꜱ:

ʏ = 4 ᴄᴏꜱ[ (2/5)(x - ᴅ) ] - 3

ᴅ ɪɴᴅɪᴄᴀᴛᴇꜱ ᴛʜᴇ ꜱʜɪꜰᴛ. ᴛʜᴇ ꜱʜɪꜰᴛ ɪꜱ ᴅᴇᴛᴇʀᴍɪɴᴇᴅ ʙʏ ᴄᴏᴍᴘᴀʀɪɴɢ ᴛʜᴇ ɢʀᴀᴘʜꜱ ᴏꜰ ʏ = 4 ᴄᴏꜱ[ (2/5)(x) ] - 3 ( ɴᴏᴛᴇ ᴅ = 0 ) ᴀɴᴅ ᴛʜᴇ ɢɪᴠᴇɴ ɢʀᴀᴘʜ. ᴡᴇ ɴᴏᴛᴇ ᴛʜᴀᴛ ᴛʜᴇ ꜱʜɪꜰᴛ (x ᴄᴏᴏʀᴅɪɴᴀᴛᴇ ᴏꜰ ᴘᴏɪɴᴛ ᴀ) ᴅ = - π/5 ꜰʀᴏᴍ ᴛʜᴇ ɢʀᴀᴘʜ (ᴏɴᴇ ꜱᴍᴀʟʟ ᴅɪᴠɪꜱɪᴏɴ ᴛʜᴇ ᴛʜᴇ ʟᴇꜰᴛ). ʜᴇɴᴄᴇ ᴛʜᴇ ᴇQᴜᴀᴛɪᴏɴ ᴏꜰ ᴛʜᴇ ɢʀᴀᴘʜ ɪꜱ:

ᴡᴇ ɴᴏᴡ ᴄʜᴇᴄᴋ ᴛʜᴀᴛ ᴛʜᴇ ꜰᴜɴᴄᴛɪᴏɴ ꜰᴏᴜɴᴅ ᴄᴏʀʀᴇꜱᴘᴏɴᴅꜱ ᴛᴏ ᴛʜᴇ ɢɪᴠᴇɴ ɢʀᴀᴘʜ ʙʏ ᴄʜᴇᴄᴋɪɴɢ ꜰᴇᴡ ᴘᴏɪɴᴛꜱ.

ᴘᴏɪɴᴛ ᴀ: x = -π/5; ᴇᴠᴀʟᴜᴀᴛᴇ ʏ ᴀᴛ ᴛʜɪꜱ ᴠᴀʟᴜᴇ ᴏꜰ x.

ʏ( - π/5)= 4 ᴄᴏꜱ[ (2/5)( - π/5 + π/5) ] - 3 = 4 ᴄᴏꜱ[ (2/5)( 0 ) ] - 3 = 1 ᴡʜɪᴄʜ ᴄᴏʀʀᴇꜱᴘᴏɴᴅꜱ ᴛᴏ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏɴ ᴛʜᴇ ɢʀᴀᴘʜ.

ᴘᴏɪɴᴛ ʙ: x = 4π + 4 π/5 = 24π/5 ( 4 ꜱᴍᴀʟʟ ᴅɪᴠɪꜱɪᴏɴ ᴀꜰᴛᴇʀ 4π)

ʏ( 24π/5 )= 4 ᴄᴏꜱ[ (2/5)( 24π/5 + π/5) ] - 3 = 4 ᴄᴏꜱ[ (2/5)( 25π/5) ] - 3 = 4 ᴄᴏꜱ[ (2/5)( 5π) ] - 3 = 4 ᴄᴏꜱ[ (2π) ] - 3 = 1

ᴡʜɪᴄʜ ᴄᴏʀʀᴇꜱᴘᴏɴᴅꜱ ᴛᴏ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏɴ ᴛʜᴇ ɢʀᴀᴘʜ.

Answer 2

Answer:

ur answer

Step-by-step explanation:

Red Indian is an offensive term for a native North American. In North America, the term is now considered a racial slur.