+1 862 207 3288 value theorem
Q1. Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.
f(x) = 8×3 – 10×2 + 3x + 5; [-1, 0] a. f(-1) = -16 and f(0) = -5; no b. f(-1) = -16 and f(0) = 5; yes c. f(-1) = 16 and f(0) = -5; yes d. f(-1) = 16 and f(0) = 5; no
Q2. Use the graph to find the vertical asymptotes, if any, of the function.
a. y = 0 b. x = 0, y = 0 c. x = 0 d. none
Q3. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function.
f(x) = x4 + 2×2 – 3 a. -4 and 4 b. -3 and 3 c. -6 and 6 d. -5 and 5
Q4. Give the equation of the oblique asymptote, if any, of the function.
h(x) = a. y = 4x b. y = 4 c. y = x + 4 d. no oblique asymptote
Q5. Find the power function that the graph of f resembles for large values of |x|.
f(x) = -x2(x + 4)3(x2 – 1) a. y = x7 b. y = -x7 c. y = x3 d. y = x2
Q6. Find the domain of the rational function.
g(x) = a. all real numbers b. {x|x ≠ -7, x ≠ 7, x ≠ -5} c. {x|x ≠ -7, x ≠ 7} d. {x|x ≠ 0, x ≠ -49}
Q7. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = 2×2 – 2x a. minimum; – b. minimum; c. maximum; – d. maximum;
Q8. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x2 – 2x – 5 a. maximum; 1 b. minimum; 1 c. maximum; – 6 d. minimum; – 6
Q9. Find the vertex and axis of symmetry of the graph of the function.
f(x) = -3×2 – 6x – 2 a. (-1, 1) ; x = -1 b. (2, -26) ; x = 2 c. (1, -11) ; x = 1 d. (-2, -8) ; x = -2
Q10. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
f(x) = 3×4 – 6×3 + 4×2 – 2x + 1 a. no real roots; f(x) = (x2 + 1)(3×2 + 1) b. 1, multiplicity 2; f(x) = (x – 1)2(3×2 + 1) c. -1, 1; f(x) = (x – 1)(x + 1)(3×2 + 1) d. -1, multiplicity 2; f(x) = (x + 1)2(3×2 + 1)
Q11. Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3×4 + 4×3 + 13×2 + 16x + 4 a. f(x) = (3x – 1)(x – 1)(x + 2)(x – 2) b. f(x) = (3x + 1)(x + 1)(x + 2i)(x – 2i) c. f(x) = (3x – 1)(x – 1)(x + 2i)(x – 2i) d. f(x) = (3x + 1)(x + 1)(x + 2)(x – 2)
Q12. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = a. symmetry with respect to the y-axis b. symmetry with respect to the origin c. neither
Q13. Find the indicated intercept(s) of the graph of the function.
x-intercepts of f(x) = a. (5, 0) b. c. d. (-5, 0)
Q14. Solve the equation in the real number system.
x4 – 3×3 + 5×2 – x – 10 = 0 a. {-1, -2} b. {1, 2} c. {-1, 2} d. {-2, 1}
Q15. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1. a. -3 b. -2 c. 3 d. 2
Q16. Find the domain of the rational function.
f(x) = . a. {x|x ≠ -3, x ≠ 5} b. {x|x ≠ 3, x ≠ -5} c. all real numbers d. {x|x ≠ 3, x ≠ -3, x ≠ -5}
Q17. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = -x2 – 2x + 2 a. minimum; – 1 b. maximum; 3 c. minimum; 3 d. maximum; – 1
Q18. Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither.
f(x) = a. symmetry with respect to the origin b. symmetry with respect to the y-axis c. neither
Q19. Find the power function that the graph of f resembles for large values of |x|.
f(x) = (x + 5)2 a. y = x10 b. y = x25 c. y = x2 d. y = x5
Q20. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) = a. Yes; degree 3 b. No; x is a negative term c. No; it is a ratio d. Yes; degree 1
