Pre-Cal
Solve the system of equations algebraically. 4x - 4y = -48 5x - 6y = -65
(-7, 5)
Describe the set of numbers using interval notation. x > 8 or x ≤ 2
(-∞, 2] ∪ (8, ∞)
Which statement is true for the graph of f(x) = 2x^3 - 6x^2 - 48x + 24?
(4, -136) is a relative minimum; (-2, 80) is a relative maximum
Solve the system of equations by using elimination -8a + 7b = -69 -3a - 3b = -9
(6,-3)
Solve the system of equations by using substitution 6r + 7s = -1 2r +4s = -12
(8,-7)
Find (f + g)(x) and (f g)(x) for f(x) = 6x^2 + 5 and g(x) = 7 - 5x.
(f + g)(x) = 6x2 - 5x + 12 (f g)(x) = 6x2 + 5x - 2
Find (f • g)(x) and (f • g)(x) for f(x) = 15x2 + 19x + 6 and g(x) = 5x + 3.
(f • g)(x) = 75x^3 + 140x^2 + 87x + 18 (f • g)(x) = 3x + 2
Simplify i^2
-1
Determine between which consecutive integers the real zeros of f(x) = 3x^3 - 5x^2 + 5x +7 are located on the interval [-10, 10]. If the zero occurs at an integer, write the integer.
-1 < x < 0;
Simplify the expression 8-8i √5 / 6+2i √5 by using complex conjugates to write quotients of complex numbers in standard form.
-4/7 - 8/7i √5
Simplify the expression (3 - 3i)^3 by performing operations with pure imaginary numbers and complex numbers.
-54 - 54i
Find the average rate of change of f(x)= √x+6 on [4,9]. Round your answer to the nearest hundredth.
0.14
Use set notation to denote the elements, subsets, and complements of the following given sets. N is the set of odd natural numbers greater than 11 and less than 21. Use set notation to write the elements of N.
N = {13, 15, 17, 19}
Consider the quadratic function f(x) = -2x^2 + 4x + 2. Find the y-intercept and the equation of the axis of symmetry.
The y-intercept is 2. The equation of the axis of symmetry is x = 1.
Find the variance and standard deviation of the given set of data to the nearest tenth. {530, 150, 320, 500, 200, 690, 770}
Variance = 48,326.5 , Standard deviation = 219.8
Find 3[ 5 6 ] -2[ 0 2 ] [-9 -2] [ -6 -4]
[ 15 14 ] [ -15 2 ]
How many ways can 5 different books be stacked on a shelf?
120
Simplify the expression: (7 + 9i)(8 - 10i).
146 + 2i
9 - 19i 12 - 5i
203 - 183 i 169 169
Jeffery surveyed 50 randomly selected workers at a factory. He collected data about the individual output of a worker on an average day. The results are shown using the box-and-whisker plot. What percent of workers have output more than 70 units?
25%
Find the interquartile range of the data shown on the box-and-whisker plot below.
29
Find the upper quartile of the data shown on the box-and-whisker plot below.
56
Use characteristics to describe the following matrix. Use A = [10 4 11 12] to find the value of A🔽21. [6 3 2 8]
6
Simplify √72x^5 y^12
6x2 y^6 √2x
Simplify 4^√6,561a^12 b^8
9a^3 b^2
Find intersections and unions of the following given sets. Use the Venn diagram to find A ∪ B, C ∩ D, and (A ∪ C) ∪ D .
A ∪ B = {2, 5, 6, 7, 8, 15}; C ∩ D = {15, 21}; (A ∪ C) ∪ D = {2, 3, 5, 7, 11, 15, 21, 26}
Use the graph below to find the domain and range.
D: (-9, -1], (0, 4] R: (-6, 8.6]
Find the exact solution of -x^2 + 7x + 5 = 0 by using the Quadratic Formula.
NOT 7-√69/-2 , 7+√69/-2
In a race between 18 people, how many ways can the top 5 finishers be arranged?
NOT 8,568
State the domain of f ° g. Then find f ° g, including any additional restrictions necessary in the domain of the composition. f(x) = -7/x g(x) = √x+3
NOT D: x ≥ -3; (f ° g)(x) = -7 /√x + 3 D: x ≠ 0; (f ° g)(x) = -7 /√x + 3
Which region in the graph below is the solution of the system of inequalities given below? y ≤ x + 5 y ≥ -x - 8
NOT Region 3
State whether the graph of -4 / x^2 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.
NOT The function is continuous.
Use the graph of f(x) to estimate f(3).
NOT f(3) = -9
Describe the end behavior of the graph.
NOT f(x)→ -∞ as x → -∞ and f(x)→ -∞ as x → +∞
Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its domain. f(x) = x - 7 / x + 4
NOT f^-1 (x) = 4x + 7 /1 - x
Given f(x) = x^2 - 3 and g(x) = x + 2 / x. Find (g ° f)(4).
NOT -6
Solve the following system of equations. State whether the system is consistent and independent, consistent and dependent, or inconsistent. -4x + 7y = 28 4x - 7y = 32
inconsistent
For which interval(s) is the function increasing and decreasing? y = | 2x^2 + x-6 |
increasing for -2 < x < 0 and x > 3/2; decreasing for x < -2 and 0 < x < 3/2
For which interval(s) is the function increasing and decreasing? y = 3x^3 - 16x + 2
increasing for x < -4/3 and x > 4/3; decreasing for -4/3 < x < 4/3
Consider f(x) = -4x^2 + 24x + 3. Determine whether the function has a maximum or minimum value. Then find the value of the maximum or minimum.
maximum; 39
Simplify the expression. x^4/7 * x^3/7 ---------------- x^1/7
x^6/7
Use the graph below to identify the y-intercept and zeros.
y-intercept: 9 zeros: 1, -1, 3, -3
Use the domain and range of each of the following relations to determine which is a function.
{(-4, 3), (-2, -1), (-7, 8)}
