Question

3. Let f(x) 3x2+2x -4. a. Is f even, odd or neither? Explain how you know. b. Find and simplify the difference quotient for fx). rite a function in slope-intercept a. Slope-4, passing through (1,4) b. Passing through (2,3) and (-1,5) c. Passing through (23) and perpendicular to the line whose equation is 3x-4y + 10-0. d. Passing through (3,4) and parallel to the line whose equation is x-1. 4. W form whose graph satisfies the given conditions. [16]

I got as far as f (x+h)-f (x)/h... pls help

Answer 1

f(x) = -3 x^2 + 2 x - 4 If function is even then f(-n) = f(n) If odd then f(-x) = f(x) First plug x = -x f(-x) = -3 (-x^2) + 2(-x) - 4 = -3 x^2 - x - 4 f(-x) = -3 x^2 - x - 4 Here f(x) notequalto f(-x) \r\n also f(-x) notequalto - f(x) therefore f(x) is not even nor odd function (b) difference quotient lim_n rightarrow 0 f(x f^n) - f(x)/n lim_n rightarrow 0 -3 (x + n)^2 + 2 (x + n) - 4 - (-3 n^2 + 2n -4)/n lim_n rightarrow 0 -3x^2 - 3n^2 - 6xn + 2x + 2n -4 + 3x^2 - 2x + 4/n lim_n rightarrow 0 n (-3n - 6x + 2)/n = lim_n rightarrow 0 3n - 6x + 2 - 6x + 2 \r\n slope m = -4 at point (1,0) so equation of line y - 4/ x - 1 = -4