Question

I'LL GIVE MEDAL HELP
Which transformation causes the described change in the graph of the function y=cos x?
1. Which one results in a horizontal shrink?
A. Cos (x/5)
B. 9cos(x)
C. Cos(3x)
D. Cos(x+2)

2. Which one results in a horizontal stretch?
A. 2/7cos(x)
B. -3cos(x)
C. Cos(7x)
D. Cos (x/3

3. Which one results in a vertical shrink?
A. Cos(x-2)
B. 2/3cos(x)
C. Cos(4x)
D. 2cos(x)

4. Which one results in a vertical stretch?
A. 1/3cos(x)
B. Cos(x+4)
C. Cos(-5x)
D. -5cos(x)

Answer 1

@Data_Lg2 @sammixboo @sweetburger @zepdrix @zzr0ck3r

Answer 2

To be honest... i'm really not sure about my answers...

Answer 3

Im going to do a little research and come back

Answer 4

Alight

Answer 5

Alright *

Answer 6

Sorry i just started learning this stuff a couple weeks ago so i dont know the answers... but i found this site. It might help

Answer 7

http://www.regentsprep.org/regents/math/algtrig/ATP9/funclesson1.htm

Answer 8

Thank you

Answer 9

YourWelome

Answer 10

did it help @Jaylokss

Answer 11

Not really :/ @moldybubblegum12

Answer 12

oh D:

Answer 13

horizontal stretch/compression in any function occur when we manipulate the input of our function (so modify our x) prior to the effects of the overarching function which is cosine in this case. If the modification occurs outside the overarching function, that is a vertical stretch or compression.

Thus cos(2x) or cos(x/5) is an example of horizontal compression and stretching respectively since we change the input of the cosine function first before we apply cosine.
Our original function must occur in half the domain for cos(2x) and 5 times the domain for cos(x/5). ***So notice the larger that factor is above 1, the more you compress the graph horizontally. The smaller the factor from 0 to 1, the more you stretch the graph horizontally.

Vertical stretch and shrinking involves multiply the overarching function by a constant factor. This factor does not affect the input as it is not directly linked to x by itself and thus only changes the y value.

y = 2 cos(x) stretches vertically by two times and y = 1/2 cos(x) shrinks it in half.
***So bigger the factor more stretch, smaller factor, smaller stretch.

In general
\[y = a \cos(bx)\] exhibits a vertical stretch/compression by factor a and horizontal compression, stretch for factor b.