Question

The function g(x) represents f(x) = 9 cosine (x minus StartFraction pi Over 2 EndFraction) + 3 after translating StartFraction pi Over 6 EndFraction units left and 4 units up.

Which equation represents g(x)?

Answer 1

Answer:

B

Step-by-step explanation:

Im almost sure it B but if not then its for sure D.

Answer 2

The equation that represents the function g(x) is $g(x)=9cos(x-\frac{\pi }{3} )+7$.

What is function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

What is translation?

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

The function is given as

$f(x)=9cos(x-\frac{\pi }{2} )+3$

The function f(x) is first translated $\frac{\pi }{6}$ units left.

The rule of translation is:

$(x,y)=(x+\frac{\pi }{6},y)$

So, we have:

$f'(x)=9cos(x+\frac{\pi }{6} -\frac{\pi }{2} )+3$

Take LCM

$f'(x)=9cos(x+\frac{\pi-3\pi }{6} )+3$

$f'(x)=9cos(x-\frac{2\pi }{6} )+3$

$f'(x)=9cos(x-\frac{\pi }{3} )+3$

Next, translate f'(x) 4 units up.

The rule of this translation is:

$(x,y)=(x,y+4)$

So, we have:

$g(x)=9cos(x-\frac{\pi }{3} )+3+4$

$g(x)=9cos(x-\frac{\pi }{3} )+7$

Hence, the equation that represents the function g(x) is $g(x)=9cos(x-\frac{\pi }{3} )+7$.

Find out more information about function and translation here

https://brainly.com/question/21145944

https://brainly.com/question/23961993

#SPJ3