1. Problem: Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. 2. (a) $f(x) = \sqrt[5]{x} = x^{\frac{1}{5}}$ is a root function because it can be expressed as a fractional power function where the exponent is $\frac{1}{5}$. 3. (b) $g(x) = \sqrt{1 - x^2} = (1 - x^2)^{\frac{1}{2}}$ is a root function since it involves a square root of an expression. It's also algebraic because it can be formed using polynomials and roots. 4. (c) $h(x) = x^9 + x^4$ is a polynomial function. The highest power of $x$ is 9, so it is a polynomial of degree 9. 5. (d) $r(x) = \frac{x^2 + 1}{x^3 + x}$ is a rational function since it is a ratio of two polynomials. It's also algebraic because rational functions are a subset of algebraic functions. 6. (e) $s(x) = \tan 2x$ is a trigonometric function because it uses the tangent trigonometric function. 7. (f) $t(x) = \log_{10} x$ is a logarithmic function with base 10. Final classifications: - $f(x)$: Root function - $g(x)$: Root function, algebraic - $h(x)$: Polynomial, degree 9 - $r(x)$: Rational and algebraic - $s(x)$: Trigonometric function - $t(x)$: Logarithmic function