Algebra Questions

1a 10 4 2a 4x 12 3a 8 X 2 1b 6 8 Do Now 11 29 1c 4 6 2b 3x 4 11 3b 12 2x 4 1d 3 2 8 2

For f x x and g x x 8 find the following composite functions and state the domain of each a fog b gof c fof d gog a fog x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain off og is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to sepa B The domain of fog is all real numbers b gof x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain of g ofis x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to sepa OB The domain of g of is all real numbers 0 fo f x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain off of is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to sepa OB The domain of f of is all real numbers d gogxx Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain of g og is x

Let G be a group with G pq where p and q are prime Prove that every proper subgroup of G is cyclic

9 5 6i 4 7i 11 10 Section 3 3 What must be added to both sides of the equation to solve by completing the square Solve for x by using the Completing the Square method x 24x 17 9 3i 12 x 16x 36

7 x 12 5 3 5x 40 65 5 x 12 X 7 12 5 subrtaction mulipication x 12 5 7 subtraction addition divison addition x 19 5 x 40 65 3 5 x 11 614 X 12 5 X 7 X 7

16 12 2x

Equation 2x 4 35 x 3 45 8 43 7 x 12 5 Operation Guided 1 Step Equations Practice Inverse Operation Work make sure to rewrite equation

d 32 3 4 x 6 a 2 b 10 c 2 d 10 d 16 4 12 x 10 a 2 b 22 c 22 d 2

No Calculator Solve for the unknown variable in each of the problems below showing your work 2 8 2x 1 x 8 4 a 5 b 2 c 4 a 4 b 4 c 16

10 9 1 2 4 8 4 3 2 1 0 2 10 3 2 3 4 3 20 4

Leaming Target I can solve one step equations for the unknown variable value Name the operation that is the inverse opposite of a Addition b Subtraction c Multiplication d Division Example 1 Work 5 x 20 Explanation

Simplify each expression 35m 65n 10 28n 4n 1 A 10m n 1 C 3 n 3 n 1 3n 5m 50n 80 B D n 1 n 9 3 An n 8 2 2 7r 70 5r 39r 54 35r 42 10r A C r 1 r 8 7 6 r 3 B r 10 9 10r D r 5

B 3 21n 53n 8 20n 10n 6n 13n 8 42n 6 5n 3 C 70n A B D 9 Sn 9 n 2 8 44 6v 63y 9v 35v 5 Sv 45 v 3 A 7 C v 9 v 4 2 3 v 9 D 7 v 6 B

8 12 8

3 5x 40 65 5 x 12

Example 2 Work 4x 3 5 4 Expl

Consider the following f x x 4x 4 a Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero Select all that apply O 2 1 O 1 0 0 1 1 2 O 3 4 X b Adjust the table to approximate the zeros of the function Use the zero or ro list Round your answers to three decimal places feature of the graphing util to verify your results Enter your answers as a comma separated

You construct an open box from a square piece of material 36 inches on a side by cutting equal squares with sides of length x from the corners and turning up the sides see figure 36 2x a Write a function V that represents the volume of the box V x 36 v x 2 b Determine the domain of the function V Enter your answer using interval notation 0 00 c Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V x V x in x in 1 2 3 K

12 2

10 2 4 10

N 10

9 12 20

7 86

6 4 8

5 12 10

21 6

3 20 4

E 01 2

7 MS 176

Identify the asymptote of the given function f x 4 6 Oy 1 Oy 1 Oy 4 Oy 6

What type of function is Oexponential decay exponential growth 0 1 x 2

What type of function is f x 3x 2 exponential decay exponential growth

Choose the best description of the function shown 4 3 2 f x y 5 4 3 2 1 1 2 3 1 2 3 4 5 O exponential decay exponential growth

Identify the asymptote for the exponential function shown f x 5 4 3 2 1 Ox 1 Oy 1 Oy 0 4 3 32 2 1 2 3 4 5 1 2 3 4 5

Identify the asymptote of the given function f x 2x 4 y 8 Oy 4 Oy 2 Oy 4 2x 48

Identify the asymptote of the exponential function shown 5 4 3 2 1 Ox 0 Oy 1 Oy 0 Ox 1 4 3 N 1 1 2 3 4 5 v x 1 2 3 4 4 5

Identify the asymptote for the given functio f x 3 2 Oy 3 Oy 2 Ox 3 y 1

Identify the asymptote of the exponential function shown below 5 4 3 2 1 Ox 3 Oy 2 Ox 1 5 3 432 1 T 3 4 5 1 2 3 4 5 g x

Choose the best description of the function showr 5 4 3 2 1 5 43 3 2 1 1 A to Ay 3 5 1 2 3 4 5 exponential growth O exponential decay g x

Consider the first six terms of a sequence shown in the graph Which equation below explicitly defines the sequence O O an 6 2n 1 an 32 16n 16 1 an n n 1 6 1 17 16 15 14 13 12 11 10 9 8 7 5 4 2 an 1 2 3 4

Consider the explicit definition of a sequence an 12 3 1 Which table of values could represent a partial sequence described by the relation n an n an n 1 4 1 12 1 2 48 2 36 2 3 576 3 108 3 4 6912 4 324 4

Given that the sequence is geometric a 3 i e the first term is 3 and the common ratio is 4 find a12 i e the 12th term a12 132 12 144 12 12 582 912 a 12 50 331 648

Consider the first six terms of this sequence 6 12 24 48 96 Which equation below recursively defines the sequence O an 67 A 6 ax 1 ax 3 2 ax 2 ax 1

Consider the pattern Which function represents the sequence that represents the number of unit squar in the pattern after each step Oa 4 x 1 O 4 2 1 9 a 41 2 a ax

Consider the first six terms of this sequence 3 6 12 24 48 96 What would be the 19th term of this sequence 393 216 786 432 1 572 864

Find mzz 5 mZZ X Write your answer as an integer or as a decimal rounded to the nearest tenth

And UV V70 Write your answer as an integer or as a decimal rounded to the nearest tenth Submit

Solve the right triangle H 3 10 H m I m H 9 Write your answers as integers or as decimals rounded to the nearest tent O I

Graph the image of kite ABCD after a dilation with a scale factor of 4 centered at the origin 10 8 6 4 D 2 104 8 6 4 2 2 4 6 8 C A 2 B 4 6 8 Ao 10 Ver en espa ol

Find WX 3 WX V 56 Write your answer as an integer or as a decimal rounded to the nearest tent