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

The function you provided is a **polynomial function**: \[ f(x) = 5x^4 - 2x^2 + 7 \] **Properties of Polynomial Functions:** 1. **Continuity:** Polynomial functions are continuous everywhere on the real number line. This means there are no breaks, holes, or asymptotes in their graphs. 2. **Domain:** The domain of a polynomial is all real numbers, \( (-\infty, \infty) \). **Conclusion:** Since \( f(x) \) is a polynomial, it is continuous for all real numbers. **Interval Notation:** \[ (-\infty, \infty) \] This indicates that \( f(x) \) is continuous for every real number \( x \).