Identify the range of the function with the given domain.
x+3y=-8 Domain x¡Ý0
Domain X is greater than or equal to 0
if x = 0, y = -8/3
if x = 1, y = -9/3
if x = 2 , y = -10/3
if x = huge, y = (-8-huge)/3
which is -even more huge
so
the range is from -8/3 including -8/3 to -infinity
To find the range of the function, you need to solve the equation for "y" in terms of "x". Let's rearrange the equation:
x + 3y = -8
3y = -x - 8
y = (-x - 8)/3
Now we have the equation in the form of y = f(x), where f(x) is (-x - 8)/3. Since the domain x ≥ 0, we need to find the range of the function for x values greater than or equal to zero.
By observing the function, we can see that as x increases, y decreases. Additionally, there are no restrictions on the possible values of y. Therefore, the range of the function is all real numbers.
In interval notation, the range would be (-∞, ∞).
To identify the range of the function, we need to solve the given equation for y and consider the restriction x≥0. Let's rearrange the equation:
x + 3y = -8
Subtract x from both sides of the equation:
3y = -8 - x
Divide both sides of the equation by 3:
y = (-8 - x) / 3
Now, let's consider the condition x≥0. Since x is greater than or equal to 0, the expression inside the parentheses (-8 - x) should be at its largest value. This occurs when x = 0.
Substitute x = 0 into the equation:
y = (-8 - 0) / 3
y = -8 / 3
Therefore, the range of the function with the given domain is y = -8/3.