Question

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
f(x)=-5.8sinx
g(x)=sinx

Answer 1

Following are a few different ways of solving this equation... Good luck!

Stretch the graph horizontally stretch by a factor of 5.

Starting with graph g and going to graph f, you'll need to multiply each x-value by 5 to produce the same y-value. You can also think in terms of the period. The period of f is 5 times greater (10 pi) than the period of g (2 pi). (Pd = 2pi/|b|).

Because the x/5 is in the bracket the stretch will concern the x-axis, and as any transformation in the x-axis does the opposite of what is expected, diving (x/5) would stretch the graph. If it was f(x)=cos(5x) the graph would shrink in the x-axis.

f(x) = sin(x+pi/2) => this is sinx horizontal shift left pi/2 from zero
g(x) = sin(x+pi/3) => this is sinx horizontal shift left pi/3 from zero
from g(x) to f(x) => pi/3 - pi/2 = -pi/6 (left)

f(x) = -2cos7x => this function period is 2pi/7
g(x) = cos x => this function period is 2pi
from g(x) to f(x) => so, it is Horizontal shrink by a factor 1/7

for your reference:
y = a sin b(x±h) ± k
a : amplitude => take absolute value
b : angular frequency
h : horizontal shift ( phase shift). (+ left, - right)
k : mid. line or vertical shift ( + up, - down)
period = 2π/b ( for sines, cosines. if tangent : p = π/b)

Answer 2

I have four answer choices, can you tell me which answer it is, please?
a.Vertical stretch by a factor of 5.8, reflection across y-axis
b. Vertical stretch by a factor of 5.8, reflection across x-axis
c. Horizontal stretch by a factor of 5.8, reflection across x-axis
d. Horizontal stretch by a factor of 5.8, reflection across y-axis

Answer 3

im 80% sure its C. lol (and its definitely not a or b... ur choice)

Answer 4

ok im going to go with your answer, thanks again