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MATH 1050-006 Practice exam 2 1. 6 points Decide whether the following statements are true or false. 100 (a) L5=500 (b) =y (x+y) + . 4 x (e) (2)2X (d) (e) 3 + 6x 9x 2 (f) 2 + x + 1 has 2 different roots. x — x + 1 has 5 different roots. 2. 4 points Caleulate.(Write the answer as a single real number) 41000 (a) 4999 (b)Z 3. 4 points Solve for x where —8=rO. 5 (a) (x+2) (b) iEfl-3=O. 4. 4 points Find the implied domains of the following expressions: (a) (b) 5. 3 + 2x x /2x — — 1 1 2 points If f(x) is an invertible function, and f(7) = 6. 4 points Find the inverse of the following fnnctions. Page 3 10. What is f_1(10)? (a) f(x)=(x-1) (b) g(x) /2x — 1+5 7. 6 points Divide. (a) (b) 4 6x — 8. — 5x + 9 +2 2 3x — 2 x — — (c) 3 + 16x 9x 2 9 2 2x + x + 1 2 x—2 4 points Complete the squares (into the form a(x + c) 2 + d): (a) —2x +6x+1 2 (b) 8x +16x+8 2 Page 4 9. 10. 2 points What’s the slope of the line passing through (—1,3) and (6,7)? 6 points Completely factor the following polynonuals.(Your answers should consist of a product of a real number. monic linear polynomial(s), and monic quadratic polynomial(s) without root) (a) 3x + 7 (b) 12_41+4 (c) x — 312 + 3x — 2(hint: factors of degree 0 coefficients are possible roots) 11. 1 points How many roots do the following polynomials have? 12. (a) 2 (b) 12 + 2x — 10 +r+5 I points Find the roots of the polynomial x2 + 3x — 1. 13. 4 points List all the monic linear factors that you know from the graph below. a 14. 37 points Graph the following functions as precisely and clearly as possible, and write down required numbers/coordinates (Might include x-,y-intcrccpt, and/or the vertex. See answer sheet for details.): (a) f: [-1, cc) [0, cc), f(x) = 5 (b) f:lR—*IR,f(x)=x (c) f:R—*IR,f(x)=---x+4 (d) 2 f:IR—>IR,f(x)=—x + 4x+4 :R-{-2} —*R.f(x) = (e) f (f) g : H R.g(x) = (I — x(r + i)(x + 3) 2 i) Page 5 Scratch paper Page 6