what are the domain and range of th function y= 2√3x+4-5?
Need HELP, ASAP
Thanks
To determine the domain and range of the function y = 2√(3x+4) - 5, we need to analyze the restrictions on the variable x and the resulting values of y.
To find the domain, we need to identify any values of x that can cause an undefined or imaginary result. In this case, since we are taking the square root of (3x+4), we need to ensure that the expression inside the square root is greater than or equal to zero, since the square root of a negative number results in an imaginary number.
So, we set the expression 3x+4 ≥ 0 and solve for x:
3x+4 ≥ 0
3x ≥ -4
x ≥ -4/3
Therefore, the domain of the function is x ≥ -4/3, meaning that x can take any value greater than or equal to -4/3.
To find the range, we need to determine all possible values of y. The square root function (√) can only yield non-negative values, so the minimum value of √(3x+4) would be 0. Subsequently, when we subtract 5 from it, the minimum value of y would be -5.
Therefore, the range of the function is y ≥ -5, indicating that y can take any value greater than or equal to -5.
In summary:
Domain: x ≥ -4/3
Range: y ≥ -5
If you have any further questions or need additional assistance, feel free to ask.
Hey there! I'd be happy to help you out ASAP. Before we get into the domain and range of the function, let's simplify it a bit, shall we?
The function y = 2√3x + 4 - 5 can be rewritten as y = 2√3x - 1.
Now, let's start with the domain. The domain refers to all possible values of x that make the function defined. In this case, we have a square root function, and we know that the radicand (the expression inside the square root) cannot be negative. Since we have 3x inside the square root, we need 3x to be non-negative.
To ensure 3x is non-negative, we can set 3x ≥ 0. Dividing both sides of the inequality by 3 (since 3 is positive), we get x ≥ 0.
So, the domain of the function is all real numbers greater than or equal to 0.
Now, onto the range. The range refers to all possible values that y can take. Since we have a square root function, the range will be all non-negative real numbers or y ≥ 0.
In summary, the domain of the function y = 2√3x - 1 is x ≥ 0, and the range is y ≥ 0.
Hope that helps! Let me know if you have any more questions or if there's anything else I can do for you.
To find the domain and range of the function y = 2√(3x+4) - 5, we need to consider the restrictions on the variable x and the resulting values of y.
1. Domain:
The domain of the function represents all possible values that x can take on. In this case, the expression under the square root (3x+4) should not produce a negative number, as taking the square root of a negative number is undefined. Therefore, we need to solve the inequality 3x+4 ≥ 0 to determine the valid values for x.
First, subtract 4 from both sides of the inequality:
3x+4-4 ≥ 0-4
3x ≥ -4
Next, divide both sides of the inequality by 3 (keeping in mind that division by zero is undefined):
(3x)/3 ≥ (-4)/3
x ≥ -4/3
So, the domain of the function is all values of x greater than or equal to -4/3, or in interval notation: [ -4/3, ∞ ).
2. Range:
The range of the function represents all possible values that y can take on. Since the function involves taking the square root of a quantity and subtracting 5, we consider two things:
a) The square root part will always produce non-negative values or zero.
b) Subtracting 5 from those non-negative values or zero will give us the range.
Hence, the range of the function is all values of y that are greater than or equal to -5, or in interval notation: ( -5, ∞ ).
So, the domain is [ -4/3, ∞ ) and the range is ( -5, ∞ ).
make that Range = [-5,∞)
I assume you mean
y = 2√(3x+4)-5
the domain of √x is x >= 0, so here you must have
3x+4 >= 0
x >= -4/3
That is, the domain is [-4/3,∞)
Since √(3x+4)=0 at x=-4/3, the range is [5,∞)