how do you find the domain and range of y=absolute value of x-9
then how would you find it for y=x^3+8 thank you
the domain is all real numbers.
the range is all real numbers >= 0
Think of the graph of y=x-9. It is a straight line extending all the way in both directions.
y = |x-9| is the same line, but it does not cross the x-axis when going down, but instead flips back and heads upward again.
i still don understand how do you know y=x-9 is a straight line
To find the domain and range of a function, you need to consider the possible values for the independent variable (x) and the corresponding values for the dependent variable (y).
1. For the function y = |x-9|:
Domain: The domain of a function refers to all possible values that the independent variable (x) can take. In this case, since there are no restrictions or limitations on x, the domain is all real numbers.
Range: The range of a function refers to all possible values that the dependent variable (y) can take. The absolute value of any number is always non-negative, meaning it can be zero or positive. Therefore, the expression |x-9| can only be zero or positive. So, the range of this function is all non-negative real numbers.
2. For the function y = x^3 + 8:
Domain: Again, there are no restrictions or limitations on x, so the domain is all real numbers.
Range: To determine the range, you need to examine the behavior of the function. As x approaches negative infinity, y approaches negative infinity, and as x approaches positive infinity, y also approaches positive infinity. Additionally, the function y = x^3 + 8 is an increasing function as x increases. Therefore, the range of this function is all real numbers.
In summary:
- For y = |x-9|, the domain is all real numbers and the range is all non-negative real numbers.
- For y = x^3 + 8, the domain is all real numbers and the range is also all real numbers.