1. The problem asks to classify each given function based on its type. 2. For (a) $f(x) = \sqrt[5]{x}$, this is a root function because the 5th root of $x$ can be expressed as $x^{\frac{1}{5}}$. 3. For (b) $g(x) = \sqrt{1 - x^2}$, this is also a root function since it involves the square root (a fractional exponent) of a polynomial expression. 4. For (c) $h(x) = x^9 + x^4$, this is a polynomial function. - The degree is the highest power of $x$, which is 9. 5. For (d) $r(x) = \frac{x^2 + 1}{x^3 + x}$, this is a rational function because it is the ratio of two polynomials. 6. For (e) $s(x) = \tan 2x$, this is a trigonometric function as it involves the tangent trigonometric function. 7. For (f) $t(x) = \log_{10} x$, this is a logarithmic function since it involves the logarithm. Final classifications: - (a) Root function - (b) Root function - (c) Polynomial function, degree 9 - (d) Rational function - (e) Trigonometric function - (f) Logarithmic function