Which function has the smallest minimum y-value?

fx) = 2 sin (3x + π) − 2
g(x) = (x − 3)2 − 1
h(x) >
x y
−2 3
−1 −2
0 −5
1 −6
2 −5
3 −2
4 3

The smallest minimum is attained by the function:

h(x)

Step-by-step explanation:

We are asked to find which function has smallest minimum value:

We have:

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

So, when sine function will have minimum value -1 then the function f(x) also has minimum value as -4.

( since 2×(-1)-2=-2-2= -4 )

As this function is a quadratic function and we know that:

(x-3)^2≥0 for all x.

so,

(x-3)^2-1≥ -1.

Hence, the minimum value of g(x) is -1.

   h(x) =y

x       y

−2      3

−1     −2

0     − 5

1     −6

2      −5

3      −2

4        3

Clearly from the table we could see that h(x) receives -6 as the minimum value.

Hence, the smallest minimum is attained by the function h(x).

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

answer are

step-by-step explanation: