SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
1)f(x) = -20x4 - 5x - 4
2)f(x) = -13x9 - 4x + 8
Write an equation for the linear function f satisfying the given conditions.
3)f(-1) = -5 and f(5) = 7
4)f(-1) = -5 and f(5) = 7
Find the vertex of the graph of the function.
5)f(x) = (x + 2)2 + 4
6)f(x) = -2x2 - 16x - 34
7)f(x) = 2x2 - 12x + 14
Find the axis of the graph of the function.
8)f(x) = 3x2 + 30x + 78
Write the quadratic function in vertex form.
9)y = x to power of ((2)) + 16x + 54
Write an equation for the quadratic function whose graph contains the given vertex and point.
10)Vertex (5, 5), point (7, 13)
11)Vertex (5, 1), point (0, 76)
Describe the strength and direction of the linear correlation.
12)
graphic(FP_pcal4c02_B42751233)
Determine if the function is a power function. If it is, then state the power and constant of variation.
13)f(x) = (1/2)x to power of ((4))
14)f(x) = (1/4)x to power of ((5))
Sketch the general shape of the graph for x ≥ 0. (either quadrant I or IV)
15)f(x) = - (2/7)x to power of ((4))
16)f(x) = (3/5)x to power of ((-5))
17)f(x) = 3x to power of ((1/4))
Determine whether the power function is even, odd, or neither.
18)f(x) = 10x to power of ((1/4))
19)f(x) = 9x to power of ((1/5))
20)f(x) = -4x to power of ((2/5))
21)f(x) = -11x to power of ((4/5))
Describe the end behavior of the polynomial function by finding (x→∞ is under lim)f(x) and (x→-∞ is under lim)f(x).
22)f(x) = -7x to power of ((4)) - 5x to power of ((2)) + 5
23)f(x) = x to power of ((3)) + 7x to power of ((2)) + 2x - 6
24)f(x) = x to power of ((3)) - 5x to power of ((2)) + 4x - 9
Find the zeros of the function.
25)f(x) = x to power of ((2)) - 7x + 12
26)f(x) = x to power of ((3)) - 36x
Find the zeros of the polynomial function and state the multiplicity of each.
27)f(x) = (x + 4)2(x - 1)
Graph the function.
28)P(x) = 2x(x + 2)(x + 1)
Find a cubic function with the given zeros.
29)-6, 5, -2
Divide f(x) by d(x), and write a summary statement in the form indicated.
30)f(x) = x to power of ((4)) + 4x to power of ((3)) - 2x to power of ((2)) + 4x - 3; d(x) = x to power of ((2)) + 1 (Write answer in fractional form)
Divide using synthetic division, and write a summary statement in fraction form.
31)(2x to power of ((3)) + 3x to power of ((2)) + 4x - 10/x + 1)
Find the remainder when f(x) is divided by (x - k)
32)f(x) = x to power of ((2)) + 4x + 9; k = -5
Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
33)x + 3; 5x4 + 16x3 - 3x2 + x + 4
Use the Rational Zeros Theorem to write a list of all potential rational zeros
34)f(x) = 7x3 + 11x2 + 2x - 14
Find all rational zeros.
35)f(x) = x to power of ((3)) - 6x to power of ((2)) + 5x + 12
36)f(x) = x to power of ((3)) - 8x to power of ((2)) + 11x + 20
Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
37)f(x) = x to power of ((3)) + 5x to power of ((2)) - 6x - 30
38)f(x) = x to power of ((3)) + 2x to power of ((2)) - 13x - 26
1)Degree: 4; leading coefficient: -20
2)Degree: 9; leading coefficient: -13
3)f(x) = 2x - 3
4)f(x) = 2x - 3
5)(-2, 4)
6)(-4, -2)
7)(3, -4)
8)x = -5
9)y = (x + 8) to power of ((2)) - 10
10)P(x) = 2x2 - 20x + 55
11)P(x) = 3x2 - 30x + 76
12)Strong positive linear correlation
13)Power is 4; constant of variation is (1/2)
14)Power is 5; constant of variation is (1/4)
15)
graphic(FP_2.1-2.4PracticeTes_A93251136)
16)
graphic(FP_pcal4c02_C52751912)
17)
graphic(FP_pcal4c02_CF2751918)
18)Neither
19)Odd
20)Even
21)Even
22)-∞, -∞
23)∞, -∞
24)∞, -∞
25)3 and 4
26)0, 6, and -6
27)-4, multiplicity 2; 1, multiplicity 1
28)
graphic(FP_CA3Hc03_BR1571658)
29)f(x) = x to power of ((3)) + 3x to power of ((2)) - 28x - 60
30)(f(x)/ (x to power of ((2)) + 1)) = (x to power of ((2)) + 4x - 3)
31)2x to power of ((2)) + x + 3 - (13/x + 1)
32)14
33)No
34)±1, ±1/7, ±2, ±2/7, ±7, ±14
35)4, 3, -1
36)4, 5, -1
37)-5 (rational), sqrt(6) (irrational), and -sqrt(6) (irrational)
38)-2 (rational), sqrt(13) (irrational), and -sqrt(13) (irrational)