Can you find the range of (x-1)(x+2) for [0, 1) ∪ (1, 6] ?solve said:Homework Statement
Need to find the range of 1/{(x-1)(x+2)} for [0, 6]
Homework Equations
The Attempt at a Solution
The domain is [0, 1) AND (1, 6] because 1/0 is an invalid operation. So I tried and this is what I got: [-0.5, ∞) and [0.025, ∞). Wrong, of course :)
How do I go about arriving to the right solution?
Thanks.
SammyS said:Can you find the range of (x-1)(x+2) for [0, 1) ∪ (1, 6] ?
Yes, that's correct.solve said:Hopefully I am right: [-2,0) and (0,40]
SammyS said:Yes, that's correct.
Do you see how that's related to the range of 1/((x-1)(x+2)) ?
solve said:Honestly not. Can I get a hint or something :)
Mentallic said:If the values of a variable k range between 2 to 5, then what are the possible values of 1/k?
Well no :tongue: but I see we're just going to disregard my example question since you already have the hang of it.solve said:[-0.5, infinity) and [0.025, infinity) ?Mentallic said:If the values of a variable k range between 2 to 5, then what are the possible values of 1/k?
solve said:But it's supposed to be (-infinity, -0.5] instead of [-0.5, infinity) so I was wondering how 1/0 gives negative infinity. This is what originally confused me.
Mentallic said:Well for the quadratic (x-1)(x+2) with [itex]x\in [0,1)[/itex], the range is negative. So for the reciprocal function 1/((x-1)(x+2)) it's still going to be negative, thus this is how you should quickly realize that as x approaches 1 from the left side (0.99... etc.), it should be approaching [itex]-\infty[/itex] rather than [itex]+\infty[/itex]
solve said:Whoa, this is WAY above my head. [itex]x\in [0,1)[/itex] for one. Have no idea what that's supposed to mean. Can you, please, tell me what that is? Thank You.
Mentallic said:It's nothing special, it just means the values of x in that set (0 to 1, but not including 1). It means the same thing as what Sammy posted in post #2.
For number, z, where z is between -2 and 0, what is 1/z? For one thing, isn't 1/z negative if z is negative.solve said:[-0.5, infinity) and [0.025, infinity) ?
But it's supposed to be (-infinity, -0.5] instead of [-0.5, infinity) so I was wondering how 1/0 gives negative infinity. This is what originally confused me.
SammyS said:For number, z, where z is between -2 and 0, what is 1/z? For one thing, isn't 1/z negative if z is negative.
... And if z is a negative number very close to zero, such as z=-0.001, isn't 1/z a very "large" negative number, such as -1000 ?
The range in mathematics refers to the set of all possible output values of a function. It is the collection of values that a function can produce when given different input values.
To find the range of a rational function, we need to determine the domain of the function and then plug in different values for the independent variable. The resulting values will give us the range of the function.
The domain is important because it tells us the set of input values that the function can accept. By knowing the domain, we can avoid plugging in values that are not allowed and determine the actual range of the function.
The domain of a rational function is determined by finding the values that make the denominator of the function equal to zero. These values are excluded from the domain as they would result in an undefined value for the function.
Yes, the range of a rational function can include negative values. The range is the set of all possible output values, so it can include both positive and negative numbers depending on the function.