Algebra Questions

Students in a ninth grade class measured their heights h in centimeters The height of the shortest student was 155 cm and the height of the tallest student was 190 cm Which inequality represents the range of heights a 155 h 190 b 155 h 190 h 2 155 or hs 190 d h 155 or h 190

Five less than a number is less than or equal to 6 times the number What inequality can be written to represent this statement O O O O 5 n 6n 5 n 6n n n 5 6n 5 6n

The scores of Mrs Lloyd s students on the last Algebra test are summarized by the following results Mean 76 0 Median 77 0 Range 29 The test was interrupted early due to unannounced fire drill so Mrs Lloyd de cided to give each student present that day an extra 5 points on the test IQR 12 What are the mean median range and IQR of the data set after 5 points is added to each student s test Press each hotspot Label the corresponding number below with the requested value

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i B R A 89 a b 2 3 oldu una g re a 2 3b 1 ifadesinin a de erini bulunuz RNEK 2019 8 2017 5 80177 35 2015 4

Match each function in Column I with the appropriate description in Column II amplitude 4 period 1 19 y 4 sin 3x 2 2x 3 Drag each description above to match the function below 20 y 3 sin 4x 2 21 y 2 sin 4x 3 2 phase shift 3 22 y 3 sin 2x 4 T 3 amplitude 2 period phase shift 4 11 GIE T amplitude 3 period phase shift 1 amplitude 3 period x phase shift 2 2

Determine the amplitude period any vertical translation and any phase shift of the given graph y 3 sin x The amplitude is CI

Graph the following function 1 y c OA 1 Which transformations are needed to graph the function y 4 correct answer below OB I 12 COS T 3 The graph of y cos x should be horizontally shifted to the left by OC K shrunk by a factor of 1 4 and vertically stretched by a factor of 4 D T The graph of y cos x should be horizontally shifted to the left by 3 stretched by a factor of 4 and vertically shrunk by a factor of 12 1 shrunk by a factor of and vertically stretched by a factor of 4 4 T The graph of y cos x should be horizontally shifted to the right by units horizontally Choose the units horizontally units horizontally The graph of y cos x should be horizontally shifted to the right by 3 of and vertically shrunk by a factor of units horizontally

Fill in the blanks to correctly complete the sentence below The graph of y 3 5 sin x is obtained by shifting the graph of y 5 sin x unit s

Fill in the blanks to correctly complete the sentence below The graph of y sin is obtained by shifting the graph of y sin x unit s to the

2 1 0 0 3 2 1 0 0 T X 2x X 2x y sin x Q T 3 la 2r A 0 T 2 3 3 5x 3 51 3 Drag each graph above to match the function below x 3 y sin x TC 3 1 hinihik 0 X 1 2x 1 2 Ay 1 0 1 70 3 4x 2n X 7 3 y cos x I 3 Y 2 cos X AY 3 2 1 0 0 TC y cos x TC 3 y 2 cos x 3 41 3 3 1 2 3

The function graphed to the right is of the form y c cos x y c sin x y cos x d or y sin x d where d is the least possible positive value Determine the equation of the graph C y Type an expression using x as the variable 2 1 1 Q

Graph the following function y cos x 1 Which transformation is needed to graph the function y cos x 5 answer below Choose the correct 6 OA The graph of y cos x should be horizontally shifted to the left by OB The graph of y cos x should be shifted vertically down by units units 6 OC The graph of y cos x should be horizontally shifted to the right by T 6 OD The graph of y cos x should be shifted vertically up by units units

Graph the following function T y sin x 6 Use the graphing tool to graph the function Click to enlarge graph For any answer boxes shown with the grapher type an exact answer Type the word pi to insert the symbol as needed C 2

Fill in the blanks to correctly complete the sentence below The graph of y 2 6 cos x is obtained by shifting the graph of y 6 cos x unit s

Determine the vertical asymptote s of the function If none exists state that fact x 2 x3 8x 12x f x Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The function has three vertical asymptotes The leftmost asymptote is Type equations OB The function has one vertical asymptote Type an equation OC The function has two vertical asymptotes The leftmost asymptote is Type equations OD The function has no vertical asymptotes the middle asymptote is and the rightmost asymptote is and the rightmost asymptote is

following function over a two period interval Give the period and the amplitude y sin 4x What is the period of the function y sin 4x 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression What is the amplitude of the function y sin 4x 1 Type an integer or a simplified fraction Which of the following is the correct graph of the function y sin 4x O A 8 8t OB 8 Ay 2 A X 8k O C A O D LEI G

Sketch the graph that possesses the characteristics listed below 4 0 f 4 0 f 4 5 f 0 0 f 0 0 f 0 1 f 2 0 f 2 2 Choose the correct graph below OA AY OB O C G D

1 a Use the fundamental theorem of algebra to determine the number of roots for 2x 4x 7 b What are the roots of 2x 4x 7 Show your work Answer

Find the following tan tan 0 N 8 given sin e 12 13 180 0 270 ACCO

Which of the following number lines depicts the solution to x 5 x 8 0 a Ob O c d 1 2 3 1 2 3 1 2 3 4 5 45 4 4 5 6 6 45 5 6 7 8 9 10 7 8 9 7 8 10 9 10 R R R

The standard form of the rational function R x O A Q mx b cx d a Write the rational function R x b Graph R using transformations c Determine the vertical asymptote and the horizontal asymptote of R G where c 0 is R x a O B a x n 3x 1 in standard form by writing R in the form quotient x 1 Q k To write a rational function in standard form requires long division remainder divisior O C O D Q

4 For the function H x x 2 a graph the rational function using transformations b use the final graph to find the domain and range and c use the final graph to list any vertical horizontal or oblique asymptotes G b What is the domain of the given function Select the correct choice below and if necessary fill in the answer box to complete your choice OA The domain of the given function is xlx is a real number x Type an integer or a simplified fraction OB The domain of the given function is xlx is a real number x Type an integer or a simplified fraction OC The domain of the given function is xlx is a real number x Type an integer or a simplified fraction Use a comma to separate answers as needed OD The domain of the given function is the set of all real numbers

1 f x x 3 f x h f x x h 3 x 3 h h 11 rationalize the numerator and simplify x h 3 x 3 x h 3 x 3 h x h 3 x 3

m R x 1 2 f x h f x h 1 1 x h x h x x h x x h h simplify and rationalize the nur x x h h x x h x x h x x h h x x h x x h 1 x x h x x

2 a List the possible rational zeros of the polynomial f x 2x 3x 2x 3 b Find the zeros off

Solve this system of equations 2x 4y 20 x 4

Find the vertical horizontal and oblique asymptotes if any of the given rational function 3 x 27 R x 2 x 7x 12 www y Simplify your answer Use a comma to separate answers as needed B There is no horizontal asymptote Find the oblique asymptote s if any of the function Select the correct choice below and fill in ar within your choice A The oblique asymptote s is are y Simplify your answer Use a comma to separate answers as needed OB There is no oblique asymptote

Click here to watch the video If a rational function is proper what is a horizontal asymptote of its graph

Evaluate wi6 164

Simplest form 54

If a polynomial f x has a remainder of 1 when divided by x 5 what is f 5 Answer f 5 1 x 5

5 2x5 y 1 2 xy 2 2 3

x 4 y 2 125x37 y C

4 343 7 x y N

2x y 8x448 S

7x y 7 s 9 2 9x9

XP2 5 x 4 y Ve t 3 125X Y EX A 3

3x 2 5 5 2

9 54x y x 3 12 X

Gx x y 5 2x y 4x8y

Find all complex zeros of the polynomial function Give exact values List multiple zeros as necessary f x x 14x 44x All complex zeros are Simplify your answer Type an exact answer using radicals and i as needed Use a comma to separate answers as needed

13x5 7 12 6 br

6 16 x y 6 Ne fo taxt XESCH SE Im

Write the equation of a function with zeroes at x 2 x 0 x 1 x 2 f x

8 9 4 b 34 39 hi

Find a polynomial function f x of least degree having only real coefficients and zeros as given Assume multiplicity 1 unless otherwise stated zero of 3 multiplicity 2 and zero 5i f x Simplify your answer

Write the equation of a real function with zeroes at x 4 and x 2 3 The imaginary unit should not be part of the answer f x

Given that 2 is a zero of the polynomial function f x find the remaining zeros f x x 10x 41x 50 List the remaining zeros other than 2 Simplify your answer Type an exact answer using radicals and i as needed Use a

Find a polynomial of degree 3 with real coefficients and zeros of 3 1 and 4 for which f 2 12 f x Simplify your answer Do not factor