1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DanielleElmas [232]
3 years ago
6

What are the amplitude, period, phase shift, and midline of f(x) = 2 sin(x + π) − 4?

Mathematics
1 answer:
MrRissso [65]3 years ago
6 0

\bf ~~~~~~~~~~~~\textit{function transformations} \\\\\\ % templates f(x)=Asin(Bx+C)+D \\\\ f(x)=Acos(Bx+C)+D\\\\ f(x)=Atan(Bx+C)+D \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \bullet \textit{ stretches or shrinks}\\ ~~~~~~\textit{horizontally by amplitude } A\cdot B\\\\ \bullet \textit{ flips it upside-down if }A\textit{ is negative}\\ ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis}


\bf \bullet \textit{ horizontal shift by }\frac{C}{B}\\ ~~~~~~if\ \frac{C}{B}\textit{ is negative, to the right}\\\\ ~~~~~~if\ \frac{C}{B}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{function period or frequency}\\ ~~~~~~\frac{2\pi }{B}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ ~~~~~~\frac{\pi }{B}\ for\ tan(\theta),\ cot(\theta)


with that template in mind, let's take a peek


\bf f(x)=2sin(x+\pi )-4\implies f(x)=\stackrel{A}{2}sin(\stackrel{B}{1}x\stackrel{C}{+\pi })\stackrel{D}{-4} \\\\[-0.35em] ~\dotfill\\\\ \textit{Amplitude}\implies 2 \\\\\\ \stackrel{phase}{\textit{Horizontal Shift}}\implies \cfrac{C}{B}\implies \cfrac{+\pi }{1}\implies +\pi \impliedby \pi \textit{ units to the left} \\\\\\ \textit{Period}\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{1}\implies 2\pi \\\\\\ \textit{Vertical Shift}\implies D\implies -4\impliedby \textit{4 units downwards}


now, the midline for the parent function of sin(x) is simply the x-axis, namely y = 0.

this shifted/transformed version of it, has a vertical shift of 4 units down, so the midline moved from y = 0, to y = -4.

You might be interested in
Please show work
Wewaii [24]

Answer:

D and A

Step-by-step explanation:

8. 1+8n^2-5n-7

8n^2-5n-6

9. -6-7

-13

5 0
2 years ago
I need help plz anyone I don't understand this at all.
nasty-shy [4]

Answer:

jejejjejejr

Step-by-step explanation:

uejejjejejjsjs

5 0
2 years ago
Read 2 more answers
A recipe calls for 125 cups of sugar. If jasmine wants to make 13 of the recipe, how many cups of sugar will she need?
iragen [17]

Answer: 1625

Step-by-step explanation: So if you want to make 13 of one recipe it said that in 1 recipe there's 125 cups of sugar so you need to multiply 123 by 13 so do this 125 x 13 = 1625 and then there, you have your answer 1,625 cups of sugar for 13 things of the recipe.

7 0
3 years ago
Name the digits of pi. At least 50
mars1129 [50]
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938 etc.
6 0
3 years ago
What is the greatest ten you can multiply by 2 to get close to but not over 58?
ExtremeBDS [4]

Answer:

20

Step-by-step explanation:

20 x 2 =40

40 is under 58 and the closest to 58

the next 10 is 30 and 30 x 30 is over 58 with 60

3 0
2 years ago
Other questions:
  • 25 feet equals how many inches
    7·1 answer
  • Eira created color panels for a wall using a mix of only red and blue paints. She plotted the quantities of red and blue paints
    7·1 answer
  • Will mark as brainliest to whoever first answers! Please help!
    13·2 answers
  • A) -3 · x = -21<br><br> b) -7x + 16 = 2x - 20<br> help pls
    11·1 answer
  • The sum of two numbers is 56. the sum of the smaller and 5 times the larger is 192. find the numbers.
    6·1 answer
  • Can you guys help me i'll give brainliest if you answer all of them
    13·2 answers
  • 6 = 4x + 9y ( what Y )
    14·1 answer
  • Solve the equation below. Pls include work<br><br><br><br> 28.10 = 15.5 + 5x
    9·2 answers
  • Plz help me with 9 and 10 im giveing 10 points to who ever helps me, and hurry plz QUICK
    10·2 answers
  • Beth is taking pictures outdoors during the evening. She knows that the later it is when she takes a picture, the longer her cam
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!