What is interval notation and how do you find it out of a linear equation? For examples...
3x+2=f(x)
3/x+5=f(x)
3x+2=f(x)
3/x+5=f(x)
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It sounds as though you know what the domain and range ARE, you just need help writing them in interval notation. Is that right? (Lemme just give you an easy way to write answers in interval notation. Pretend that the number line is a pasture, and your possible solutions are cows. You have to keep your cows on the part of the number line that can contain its solutions.
You have two kinds of fences. The curvy kind of fence bends, so it lets the cow step on that number where the ( is.
The square kind of fence [ is mean and electric -- the cow can not step on the number where it is.
If your answer involves positive or negative infinity, you ALWAYS use the curvy fence, cuz you don't want the cows to ever have to stop walking.
Ok, skip reading the next part if you know how to find domain and range...
The easiest way to tell the domain (what x is allowed to be) is to think about what x is NOT allowed to be. Those would be restrictions on the domain. Once you figure out what the domain is (or is NOT), then think about what that might mean to the range. Does eliminating some values of x rule out certain values of y?
3x + 2 = f(x)
Is there anything at all that we could stick in there for x (domain) that would make the planet explode? Nope! So the domain is all real numbers. If we need to express that in Interval Notation, we need to say that x can be anywhere from Negative Infinity through Positive Infinity. Remember to use curvy parentheses. Since we didn't restrict the domain, there are no restrictions on the range, f(x). Same answer.
3/(x + 5) = f(x)
Can I assume that (x+5) is the denominator? If so, then let's think about what x can NOT be. x can never be allowed to equal -5. But it can be any other number, below or above -5.
You have two kinds of fences. The curvy kind of fence bends, so it lets the cow step on that number where the ( is.
The square kind of fence [ is mean and electric -- the cow can not step on the number where it is.
If your answer involves positive or negative infinity, you ALWAYS use the curvy fence, cuz you don't want the cows to ever have to stop walking.
Ok, skip reading the next part if you know how to find domain and range...
The easiest way to tell the domain (what x is allowed to be) is to think about what x is NOT allowed to be. Those would be restrictions on the domain. Once you figure out what the domain is (or is NOT), then think about what that might mean to the range. Does eliminating some values of x rule out certain values of y?
3x + 2 = f(x)
Is there anything at all that we could stick in there for x (domain) that would make the planet explode? Nope! So the domain is all real numbers. If we need to express that in Interval Notation, we need to say that x can be anywhere from Negative Infinity through Positive Infinity. Remember to use curvy parentheses. Since we didn't restrict the domain, there are no restrictions on the range, f(x). Same answer.
3/(x + 5) = f(x)
Can I assume that (x+5) is the denominator? If so, then let's think about what x can NOT be. x can never be allowed to equal -5. But it can be any other number, below or above -5.
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