Need help with domain and range
how do you find the domain and range of
y=x+8.
after that one how do you find the domain and range of 7x+y=1
the domain of all polynomials is all real numbers
the range of all linear equations (with nonzero slope) is all real numbers.
Think about it. You have a straight line that extends all the way in both directions. Assuming it is not horizontal, then there is no value for either x or y that does not have a point on the line.
but how do you know if an equation is a straight line or not
To find the domain and range of a function, you need to consider the set of possible input values (domain) and the set of possible output values (range).
1. Domain and Range of y = x + 8:
- For the domain, you can assume that any real number can be used as an input for x in the equation y = x + 8. Hence, the domain is -∞ to +∞ (all real numbers).
- For the range, you can see that the value of y will always be greater than or equal to 8 since x is not restricted. Therefore, the range is [8, +∞).
2. Domain and Range of 7x + y = 1:
To find the domain and range of this equation, it needs to be rewritten in the form y = f(x) (solved for y).
To rewrite the equation:
- Subtract 7x from both sides: y = 1 - 7x.
- Domain: In this case, x can again be any real number because there are no restrictions. Therefore, the domain is -∞ to +∞ (all real numbers).
- Range: In this case, y can also take any real number, as there are no restrictions. Hence, the range is -∞ to +∞ (all real numbers).
In both cases, the domain covers all real numbers, while the range is unbounded on the upper side.