What are the domain and range of the function y=2square root 3x+4-5?

A.x>=-4/3;y>=-5
B.x>=4/3;y>=5
C.x<=-4/3;y<=-5
D.x>=-4/3;y>=5

I think it is A...?

Thank you

B is actually y>=-5...my mistake - do you still think it's B?

To determine the domain and range of the function y = 2sqrt(3x + 4) - 5, we need to consider the restrictions on the domain and the possible values of y.

Domain:
The function involves a square root, and the expression inside the square root must be non-negative. Therefore, we need to find the values of x for which 3x + 4 is greater than or equal to zero.

Solving for x:
3x + 4 ≥ 0
3x ≥ -4
x ≥ -4/3

So, the domain of the function is x ≥ -4/3.

Range:
In this case, we can see that the function is a translation of the square root function 2sqrt(x). The graph of the square root function starts from y = 0 and increases as x increases. In this function, we subtract 5 from the output of the square root function, which shifts the entire graph downward by 5 units. Therefore, the lowest possible value for y is -5.

So, the range of the function is y ≥ -5.

Based on the analysis, the correct answer is C) x ≤ -4/3; y ≤ -5.

To find the domain and range of a function, you need to analyze the behavior of the function and determine the possible values for the input (domain) and output (range).

In this case, the given function is y = 2√(3x + 4) - 5.

Let's start with the domain. The square root function (√) is defined for non-negative real numbers. Therefore, the expression inside the square root (3x + 4) must be greater than or equal to zero:

3x + 4 ≥ 0

Solving for x:

3x ≥ -4
x ≥ -4/3

This means that the function is defined for x values greater than or equal to -4/3.

Now, let's consider the range. Since the function involves a square root, the output (y) values must be greater than or equal to zero. However, there aren't any explicit restrictions on the possible values of y.

Based on this analysis, the correct answer is:

A. x ≥ -4/3; y ≥ -5

So, you are correct in choosing option A.