Question

Let f(x) = 7 x^{5} - 5 x^{4} + 2. use interval notation to indicate where f(x) is continuous.

Answer 1

`f(x)=7 x^(5) -5 x^(4) +2` is a polynomial function, and every polynomial function is continuous everywhere; therefore,
`f(x)` is continuous from minus infinite to infinite.
In interval notation: (-∞,∞)
Remember that in interval notation you use brackets [ ] to indicate that the end points are included, and parentheses to indicate that the end points are excluded; since infinite is not a defined point, it cannot be included, so we use parentheses.