What do the domain and range of a function compare to in a linear equation?
I do not know what the question means.
for the general case where
y = m x + b
the domain is all real x, (from -oo to +00)
and the range is all real y.
Now if you have a special case, like m = 0 (horizontal) or x = constant (vertical, well then those are special cases.
I want to say what Damon said in a different way.
In the y-intercept equation y = mx + b (an equation that represents linear functions), the domain is ALL REAL NUMBERS going from negative infinity to positive infinity; the range is also ALL REAL NUMBERS y.
Is this what you sought?
In a linear equation, the domain and range correspond to different concepts.
The domain of a linear equation refers to the set of all possible input values for the equation. It represents the values that the independent variable (usually denoted as "x") can take in the equation.
The range of a linear equation, on the other hand, refers to the set of all possible output values that the equation produces. It represents the values that the dependent variable (usually denoted as "y") can take on in the equation.
To determine the domain and range of a linear equation, we can use a few general rules:
1. For the domain: Since the independent variable can typically take any value, the domain of a linear equation is often considered to be all real numbers (-∞, ∞). However, there might be some cases where specific restrictions apply, such as when dealing with a specific context or mathematical condition, which might limit the domain.
2. For the range: To determine the range, we can often look at the slope of the linear equation. If the slope is positive (greater than 0), then the range will also be all real numbers (-∞, ∞). However, if the slope is negative (less than 0), the range will be limited to a specific interval.
It's important to note that the domain and range of a linear equation can be further restricted by specific conditions or limitations given in the context of the problem. To find the exact domain and range of a specific linear equation, it's always best to consider the given information and any additional constraints provided.