MATH 1314 - College Algebra Review for Test 3 Section 4.4 1. The graph of a 3rd, 4th, or 5th degree polynomial f (x) with integer zeros is shown at the right. Determine the factored form of f (x) . € €

2. Solve exactly for x: 7x 3 − 5x 2 − 21x + 15 = 0 . Simplify your answers including removing perfect squares from under square roots and reducing fractions, when possible. 2 3. Solve exactly € for x: x = 4 x −13. Simplify your answers including removing perfect squares from under square roots and reducing fractions, when possible. Write any complex solutions in standard form.

€ 4. Solve exactly for x: x 6 = 10x 3 − 21. Simplify your answers including removing perfect squares from under square roots and reducing fractions, when possible. Write any complex solutions in standard form. € 2 5. Find the zeros of f (x) = 7x 3 + 5x 2 + 12x − 4 given that is a zero. 7 Section 4.5 € € 6. The graph of a 5th degree polynomial f (x) is shown at the right. (a) How many different real zeros does f (x) have? €

y

3

(b) How many different imaginary zeros does f (x) have? €

€

3

x

MATH 1314 - College Algebra - Review for Test 3 (Thomason) - p. 2 of 6

7. Find the completely factored form of a polynomial f (x) with real coefficients that satisfies the following conditions: Degree 3; a3 = 2 ; zeros include 3 and 1–2i 8. Find the completely factored form of a polynomial f (x) with real coefficients that € satisfies the following conditions: Degree 4; an = −1; zeros include 0, 2, and 3i € 9. (a) Find all the zeros of f ( x) = x 3 − 3x 2 +€9x − 27 . (b) Write f (x) in completely factored form.

€ 10. (a) Find all the zeros of f ( x) = 4x 3 + 32x . (b) Write f (x) in completely factored form. € € 4 3 2 11. (a) Find all the zeros of f ( x) = 3x − 6x +12x . (b) Write f (x) in completely factored form. € € Section 4.6 € 2x€− 3 . 5x + 4 (a) What is the domain? (b) Give the x-intercept(s), if any. (c) Give the y-intercept(s), if any. (d) Give the equation(s) of the vertical asymptote(s), if any. (e) Give the equation(s) of the horizontal asymptote(s), if any.

12. Let f ( x) =

€

13. Let f ( x) =

€

. x 2 − 6x + 9 (a) What is the domain? (b) Give the x-intercept(s), if any. (c) Give the y-intercept(s), if any. (d) Give the equation(s) of the vertical asymptote(s), if any. (e) Give the equation(s) of the horizontal asymptote(s), if any. 14. Let f ( x) =

€

9x 2 −16

3x + 5

. x 2 − 2x −15 (a) What is the domain? (b) Give the x-intercept(s), if any. (c) Give the y-intercept(s), if any. (d) Give the equation(s) of the vertical asymptote(s), if any. (e) Give the equation(s) of the horizontal asymptote(s), if any. 15. Use transformations of the memorized graph for y =

1 x

y

1 to graph y = − + 2 on the coordinate system at the right. x € €

x

MATH 1314 - College Algebra - Review for Test 3 (Thomason) - p. 3 of 6

y

16. Use transformations of the memorized graph for 1 1 y= to graph y = − 4 on the coordinate system x2 ( x + 2)2 at the right.

€

x

€

17. The braking distance (in feet) for a car traveling 50 miles per hour on a wet uphill road is given 2500 by the formula D( x) = , where x is the grade (slope) of the road. If the braking distance is 30x + 9 250 feet, what is the grade of the road? Round your answer to the nearest tenth of a percent. Section 4.7 € 18. Solve for x and give your solution in interval notation: 2x 2 +15x < x 3 19. Solve for x and give your solution in interval notation: (x + 4)(x − 2)(x − 5) 2 ≤ 0 20. Solve for x:

€

2 3 + = 5 x − 4 x +1

€ 21. The graph of f (x) is shown at the right. For what values of x is f (x) ≥ 0 ? Give your answer in interval € notation. (Note: All intercepts and asymptotes occur at integers.) € €

y

1

22. Solve for x and give your answer in interval notation:

x −3 x 2 −1