1. The problem states that the function $x^{7} + x^{5} + 3x - 1$ is a polynomial function but not a power function. 2. A polynomial function is a sum of terms consisting of variables raised to whole number powers multiplied by coefficients. 3. A power function has the form $f(x) = ax^n$ where $a$ and $n$ are constants, and there is only one term. 4. The given function has multiple terms: $x^{7}$, $x^{5}$, $3x$, and $-1$, so it is a polynomial but not a power function. 5. This distinction is important because power functions have simpler behavior and graph shapes compared to general polynomials. Final answer: The function $x^{7} + x^{5} + 3x - 1$ is a polynomial function but not a power function because it contains multiple terms with different powers of $x$.