Er, this was on the review and I don't know what the deuce this means or how to go about finding it.
Help?
Help?
-
Evil things that can happen that can ruin the domain of a function:
A) Denominator equals zero
B) Taking the square root of a negative number
C) Logarithm of something that's not positive
D) Tangent of 90 degrees, 270 degrees, etc.
E) Anything that's physically / logically impossible if it's a word problem. If p(x) = the cost of x pencils, then the domain is only nonnegative integer values of x, since you can't buy half a pencil, nor can you buy -1 pencils. This is known as a "discrete" function, since its graph will consist of points, and not a straight line or a curve.
If you don't know logs or tangents yet, ignore D and/or E.
The others are pretty important. In a rational function, setting the denominator equal to zero will give places where the function is undefined. This can force you to solve a quadratic equation, like finding the domain of f(x) = 1 / (x^2 - 3x + 2). The domain of that function is all real numbers excluding 1 and 2, since x^2 - 3x + 2 = 0 leads to the factorization (x-2)(x-1) = 0.
In a rational functoin like that, the lines x=1 and x=2 for "undefined" numbers will generally be vertical asymptotes. A cool exception happens when factors cancel. If g(x) = (x-3) / (x-3), then its domain is all values of x except for x=3. The graph will be the same as the graph of g(x) = 1 since that's what you get after cancellation....but there will be a hole at (3,1).
A) Denominator equals zero
B) Taking the square root of a negative number
C) Logarithm of something that's not positive
D) Tangent of 90 degrees, 270 degrees, etc.
E) Anything that's physically / logically impossible if it's a word problem. If p(x) = the cost of x pencils, then the domain is only nonnegative integer values of x, since you can't buy half a pencil, nor can you buy -1 pencils. This is known as a "discrete" function, since its graph will consist of points, and not a straight line or a curve.
If you don't know logs or tangents yet, ignore D and/or E.
The others are pretty important. In a rational function, setting the denominator equal to zero will give places where the function is undefined. This can force you to solve a quadratic equation, like finding the domain of f(x) = 1 / (x^2 - 3x + 2). The domain of that function is all real numbers excluding 1 and 2, since x^2 - 3x + 2 = 0 leads to the factorization (x-2)(x-1) = 0.
In a rational functoin like that, the lines x=1 and x=2 for "undefined" numbers will generally be vertical asymptotes. A cool exception happens when factors cancel. If g(x) = (x-3) / (x-3), then its domain is all values of x except for x=3. The graph will be the same as the graph of g(x) = 1 since that's what you get after cancellation....but there will be a hole at (3,1).
-
The domain of an expression is all real numbers except for the regions where the expression is undefined. This can occur where the denominator equals 0, a square root is less than 0, or a logarithm is less than or equal to 0. All of these are undefined and therefore are not part of the domain.
(x-9)=0
Solve the equation to find where the original expression is undefined.
x=9
The domain of the rational expression is all real numbers except where the expression is undefined.
x≠9
(-∞,9) U (9,∞)<------------answer
Hope that helps!
(x-9)=0
Solve the equation to find where the original expression is undefined.
x=9
The domain of the rational expression is all real numbers except where the expression is undefined.
x≠9
(-∞,9) U (9,∞)<------------answer
Hope that helps!
-
f(x) = 5/(x-9)
You have a rational expression there and no rational expression can have a 0 in the denominator.
so (x-9)≠ 0 which means x≠ 9
so x can be any value as long as it's not 9
so the domain is (-∞ ,9)(9,∞ )
You have a rational expression there and no rational expression can have a 0 in the denominator.
so (x-9)≠ 0 which means x≠ 9
so x can be any value as long as it's not 9
so the domain is (-∞ ,9)(9,∞ )
-
Basically, what are the possible values of x for the equation. Since the denominator of a fraction can NOT equal 0, the domain is x =/= 9. Hope this helped. :)