Reference no: EM131582479

Question: 1. Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x², but with the given point as the vertex (5, 3).

A. f(x) = (2x - 4) + 4

B. f(x) = 2(2x + 8) + 3

C. f(x) = 2(x - 5)² + 3

D. f(x) = 2(x + 3)² + 3

2. Write an equation that expresses each relationship. Then solve the equation for y.

x varies jointly as y and z

A. x = kz; y = x/k

B. x = kyz; y = x/kz

C. x = kzy; y = x/z

D. x = ky/z; y = x/zk

3. The graph of f(x) = -x³ __________ to the left and __________ to the right.

A. rises; falls

B. falls; falls

C. falls; rises

D. falls; falls

4. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x²(x - 1)³(x + 2)

A. x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1

B. x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2.

C. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0.

D. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0.

5. Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum.

Maximum = 4 at x = -2

A. f(x) = 4(x + 6)² - 4

B. f(x) = -5(x + 8)² + 1

C. f(x) = 3(x + 7)² - 7

D. f(x) = -3(x + 2)² + 4

6. Find the domain of the following rational function.

f(x) = x + 7/x² + 49

A. All real numbers < 69

B. All real numbers > 210

C. All real numbers ≤ 77

D. All real numbers

7. Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x² - 7x + 5)/x - 4 is:

A. y = 3x + 5.

B. y = 6x + 7.

C. y = 2x - 5.

D. y = 3x² + 7.

8. Solve the following polynomial inequality.

9x² - 6x + 1 < 0

A. (-∞, -3)

B. (-1, ∞)

C. [2, 4)

D. Ø

9. The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as:

A. x - 5.

B. x + 4.

C. x - 8.

D. x - x.

10. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x⁴ - 9x²

A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0.

B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0.

C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0.

D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0.

11. The graph of f(x) = -x² __________ to the left and __________ to the right.

A. falls; rises

B. rises; rises

C. falls; falls

D. rises; rises

12. 40 times a number added to the negative square of that number can be expressed as:

A. A(x) = x² + 20x.

B. A(x) = -x + 30x.

C. A(x) = -x² - 60x.

D. A(x) = -x² + 40x.

13. Find the domain of the following rational function.

g(x) = 3x²/((x - 5)(x + 4))

A. {x¦ x ≠ 3, x ≠ 4}

B. {x¦ x ≠ 4, x ≠ -4}

C. {x¦ x ≠ 5, x ≠ -4}

D. {x¦ x ≠ -3, x ≠ 4}

14. 8 times a number subtracted from the squared of that number can be expressed as:

A. P(x) = x + 7x.

B. P(x) = x² - 8x.

C. P(x) = x - x.

D. P(x) = x² + 10x.

15. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = x³ + 2x² - x - 2

A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each.

B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each.

C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each.

D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each.

16. Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = 2(x - 3)² + 1

A. (3, 1)

B. (7, 2)

C. (6, 5)

D. (2, 1)

17. Determine the degree and the leading coefficient of the polynomial function f(x) = -2x³ (x - 1)(x + 5).

A. 5; -2

B. 7; -4

C. 2; -5

D. 1; -9

18. Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

f(x) = -2x⁴ + 4x³

A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0

B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3

C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2

D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3

19. Solve the following polynomial inequality.

3x² + 10x - 8 ≤ 0

A. [6, 1/3]

B. [-4, 2/3]

C. [-9, 4/5]

D. [8, 2/7]

20. Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = -2(x + 1)² + 5

A. (-1, 5)

B. (2, 10)

C. (1, 10)

D. (-3, 7)