Given f(x)=tan(x) and g(x)=1/x^2, , provide a characteristic that the two functions have in common and a characteristic that distinguishes them.
have you looked at the graphs?
Both have a vertical asymptote
Only g has a horizontal asymptote
You can probably see other differences as well.
To find a characteristic that the functions f(x) = tan(x) and g(x) = 1/x^2 have in common, we can observe their domain.
The domain of both functions is all real numbers except for the values that make the denominators equal to zero. For the function f(x) = tan(x), this means x cannot be equal to (2n + 1)π/2, where n is an integer. Similarly, for the function g(x) = 1/x^2, x cannot be equal to zero.
Therefore, the common characteristic of these functions is that they both have identical domains, which are all real numbers except for a few isolated points.
To find a characteristic that distinguishes these functions, we can look at their range.
The range of the function f(x) = tan(x) is all real numbers. The function oscillates between positive and negative infinity, passing through all the values in between.
On the other hand, the range of the function g(x) = 1/x^2 is all positive real numbers (excluding zero). As the function approaches zero, the value of g(x) increases dramatically, but it never actually reaches zero.
Therefore, the distinguishing characteristic of these functions is their different ranges. While f(x) = tan(x) takes on all real values, g(x) = 1/x^2 takes on all positive real values, except for zero.