10pts

compare the following functions:

f(x) = −4sin(x − 0.5) + 11 g(x)

graph of a quadratic with points at 2, 7 and 3, 6 and 4, 7 h(x)

x y

−2 14

−1 9

0 6

1 5

2 6

3 9

4 14

which function has the smallest minimum?

all three functions have the same minimum

f(x)

g(x)

h(x)

Hence the function which has the smallest minimum is: h(x)

Step-by-step explanation:

We are given function f(x) as:

We know that the minimum value attained by the sine function is -1 and the maximum value attained by sine function is 1.

so the function f(x) receives the minimum value when sine function attains the maximum value since the term of sine function is subtracted.

Hence, the minimum value of f(x) is: 11-4=7 ( when sine function is equal to 1)

x    y

−2   14

−1   9

 0   6

  1   5

 2   6

 3   9

 4   14

Hence, the minimum value attained by h(x) is 5. ( when x=1)

so, the equation will be:

Hence on putting these coordinates we will get:

a=1,b=3 and c=7.

Hence the function g(x) is given as:

So,the minimum value attained by g(x) could be seen from the graph is at the point (3,6).

Hence, the minimum value attained by g(x) is 6.

Hence the function which has the smallest minimum is h(x)

the answer is a

step-by-step explanation:

because your just changing the position of where the shape is

d

step-by-step explanation:

d