Thank you in advance

Question

Compare the functions shown below: f(x) = 3 cos 2x + 4 g(x) cosine graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3 h(x) x y -6 -11 -5 -6 -4 -3 -3 -2 -2 -3 -1 -6 0 -11 Which function has the greatest maximum y-value? f(x) g(x) h(x) All three functions have the same maximum y-value.

Answer 1

Given points for g(x) function are correct?

(0, 3pi/2)

(0, pi)

(-3, 3pi/2)

(0, 2pi)

Comments

I am not sure I understand your question? I think the answer is h(x). not too sure though

---

Too many y values for single x cordinate, so g(x) can not be a function.

 

f(x) = 3cos(2x)+4

To find the y -intercept, substitute x = 0 in the above equation.

f(0) =  3cos(2*0) +4 = 3 * 1 + 4 = 7

y-intercept of f(x) is 7

 

g(x) = It is not a function

 

The given points representing the parabola equation h(x) = ax^2 + bx + c, and parabola equation will be 3 h(x) = (-x^2 - 6x - 11)

h(x) = - (1/3) (x^2 + 6x +11)

To find the y -intercept, substitute x = 0 in the above equation.

h(0) = - (1/3) (0^2 + 6*0 +11)

h(0) =  - 11/3.

y-intercept of h(x) is -11/3

Maximum y-value at x = -b/2a = - (-2)/2*(-1/3) = -3

h(-3) = - (1/3) (-3^2 + 6*-3 +11) = -2/3 = -0.6667

 

So, f(x) has the greatest maximum y value i.e = 7