Determine the intervals on which f(x) is continuous
f(x)=15sin(x^2+71)
all polynomials are continuous for all real x
sin(x) is continuous for all real x
so, sine(polynomial) is continuous for all real x.
lol sorry I forget that
To determine the intervals on which f(x) is continuous, we need to check if the function meets certain conditions at every point in the domain.
In the case of the function f(x) = 15sin(x^2 + 71), we need to consider two aspects: the domain of the function and the properties of sine.
1. Domain of the function:
The function f(x) = 15sin(x^2 + 71) is defined for all real numbers because the sine function is defined for any input. So the domain of f(x) is (-∞, ∞).
2. Properties of sine:
The sine function is continuous everywhere, which means it has no jumps, holes, or vertical asymptotes. Therefore, if we can find any values of x for which x^2 + 71 is undefined (for example, if x^2 + 71 = 0), we need to exclude those points from the domain.
However, x^2 + 71 is defined for all real numbers, so we don't need to exclude any points. Therefore, the function f(x) = 15sin(x^2 + 71) is continuous for all real numbers x.
In summary, f(x) = 15sin(x^2 + 71) is continuous for all real values of x since both the domain of the function and the properties of the sine function allow for continuity.