Consider the functions.
f(x)= square root x
g(x)= square root x-3+1
h(x)= square root x+1-2
which statement compares the relative locations of the minimums of the functions?
1.the minimums of g(x) and h(x) are both in the first quadrant.
2.the minimums of g(x) and h(x) are both in the third quadrant.
3.the minimum of h(x) is farther right and up from the minimums of f(x) and g(x).
4.the minimum of h(x) is farther left and down from the minimums of f(x) and g(x).

The minimum of h(x) is farther left and down from the minimums of f(x) and g(x) ⇒ answer 4

Step-by-step explanation:

* Lets revise the meaning of the minimum of the function

- The minimum of a function is the lowest point of a vertex

- The minimum value is the y-coordinate of the lowest point

* Now lets solve the problem

∵ f(x) = √x

- The domain of the function is all the real numbers ≥ 0, because

 there is no square root for negative numbers

- We will use the first value of x to find the range of the function

∵ x = 0 ⇒ first value of the domain

∴ f(0) = √0  = 0

∴ The minimum of f(x) is point (0 , 0)

∵ g(x) = √(x - 3) + 1

- Lets find the domain of the function

∵ x - 3 ≥ 0 ⇒ add 3 for both sides

∴ x ≥ 3

∴ The domain of the function is all real values of x ≥ 3

- We will use the first value of x to find the range of the function

∵ x = 3 ⇒ the first value of the domain

∴ g(3) = √(3 - 3) + 1 = 0 + 1 = 1

∴ The minimum of g(x) is point (3 , 1)

∵ h(x) = √(x + 1) - 2

- Lets find the domain of the function

∵ x + 1 ≥ 0 ⇒ subtract 1 for both sides

∴ x ≥ -1

∴ The domain of the function is all real values of x ≥ -1

- We will use the first value of x to find the range of the function

∵ x = -1 ⇒ the first value of the domain

∴ h(-1) = √(-1 + 1) - 2 = 0 -  = -2

∴ The minimum of h(x) is point (-1 , -2)

* To find the correct answer look to the minimum points of the

 functions (0 , 0) , (3 , 1) , (-1 , -2)

- The minimum of f(x) lies on the origin

- The minimum of g(x) lies in the 1st quadrant

- The minimum of h(x) lies in the 3rd quadrant

∴ The minimum of h(x) is farther left and down from the minimums

   of f(x) and g(x)

- Look to the attached graph to more understand

- The red curve is f(x)

- The blue curve is g(x)

- The green curve is h(x)

i dont know

step-by-step explanation:

a

step-by-step explanation: