Classify each function as a power function, root function, polynomial (state its
ID: 2894503 • Letter: C
Question
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. (a) f(x) = 5 squareroot x (b) g(x) = squareroot 1 - x^2 (x) h(x) = x^9 + x^4 (d) r(x) = x^2 + 1/x^3 + x (e) s(x) = tan 2x (f) t(x) = log^x_10 New functions from old functions Suppose the graph of f is given, write equations for the graphs that are obtained from the graph of f as follows. (a) Shift 3 units upward. (b) Shift 3 units downward. (c) Shift 3 units to the right. (d) Shift 3 units to the left. (e) Reflect about the x-axis. (f) Reflect about the y-axis. Find f + g, f - g, f_g, f/g and state their domains. f(x) = x^3 + 2x^2 g(x) = 3x62 - 1 f(x) = squareroot 1 + x g(x) = squareroot 1 - xExplanation / Answer
(a) f(x) = x1/5 is an power function with contant power n = 1/5
(b) g(x) = sqrt(1-x2) is a root function since it contains a polynomial inside root.
(c) h(x) = x9 + x4 is a polynomial with degree 9
(d) r(x) = (x2+1)/(x3 + x) is a rational function since its in the form of p(x)/q(x)
(e) s(x) = tan 2x is trignometric function.
(f) t(x) = log10 x is a logarithmic function.