Контрольная работа по алгебра

Oraliq nazorat №1 2 -kurs

1-variant

1. For f(x) = x² + 5x – 3 , find f(4) , f( 2x-1) , f(2\x) and f( x\5) .

2. For f(x) = 3x+1 and g(x) = x² + 7x – 3 , find g(f(x)) , f(g(x)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= 5x+2 b) y= c) y= x² + 6x + 6

1. Sketch the graph of y= x² + 2x – 8.

2. (Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

2-variant

1. For the following functions, find f (-2).

1. f(x)= 2 - 3x² b) f(x)=1+ 5x - x³

1. For f(x) = 2 – 5x and g(x) = 2x² – x + 5, find g(f(2x)) , f(g(-1)).

2. What is the largest domain for which f(x) has an inverse function?

1. y= b) y= x² – 2x

1. Write f(x) = | x – 3 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

3-variant

1. For f(x) = 10 + x – 3x² , find f(-1) , f( x - 4) , f(1\3x) and f( x\2) .

2. For f(x) = 2 – x² and g(x) = 2x + 5, find g(f(-x)) , f(g(x\3)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – 4x b) y=

1. Sketch the graph of y= | 4x – 1 |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

4-variant

1. For f(x) = 3x² – 1 , find f(-2) , f( -x-1) , f(2\3x) and f( 2x\5) .

2. For f(x) = x+1 and g(x) = x² + x , find g(f(x)) , f(g(x)).

3. For each function f(x), find the inverse function f^-1(x).

a) y= x+2 b) y= c) y= -x² + 6x

1. Sketch the graph of y= x² + 4x +3.

2. (Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

5-variant

1. For the following functions, find f ( 5 ).

1. f(x)= 2 + x² b) f(x)=11 - x - 2x³

1. For f(x) = 1 + x and g(x) = 2x² – 5x + 2, find g(f(x)) , f(g(0)).

2. What is the largest domain for which f(x) has an inverse function?

1. y= b) y= 2x² – 1

1. Write f(x) = | x +1 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

6-variant

1. For f(x) = x – 3x² , find f(1) , f( x +2) , f(1\x) and f( -3x\2) .

2. For f(x) = 2x² -1 and g(x) = 2x - 1, find g(f(3x)) , f(g(2\x)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – 4x + 4 b) y=

1. Sketch the graph of y= | x – 1 |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

7-variant

1. For f(x) = 10 – 3x² , find f(-3) , f( 4x - 3) , f(3\x) and f( x\2) .

2. For f(x) = 2 + x² and g(x) = x(x + 5) + 1, find g(f(-x)) , f(g(x\3)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – 4x + 4 b) y=

1. Sketch the graph of y= | x + 1 |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

8-variant

1. For the following functions, find f (-1).

1. f(x)= 2 + x + 3x² b) f(x)=1 + 5x² - x³

1. For f(x) = 1 + x and g(x) = 2x² – x + 5, find g(f(7x)) , f(g(-7)).

2. What is the largest domain for which f(x) has an inverse function?

1. y= b) y= 2x² – 4x + 2

1. Write f(x) = | 3x – 1 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential

9- variant

1. For f(x) = 1 +x² – x³ , find f(0) , f( x - 3) , f(1\x) and f( -x\2) .

2. For f(x) = 12 + x² and g(x) = 3(x + 5) + 1, find g(f(-x)) , f(g(1\3)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – 6x + 10 b) y=

1. Write f(x) = as piecewise function.

2. Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

10-variant

1. ,For f(x) = 2x² + x – 3 , find f(-x) , f( 2x-1) , f(1\x) and f( x\2) .

2. For f(x) = -2x+1 and g(x) = -x² + 7x , find g(f(x)) , f(g(x)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= -x+2 b) y=

1. Sketch the graph of y= x² + 2x – 3.

2. (Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

11-variant

1. For the following functions, find f (-3).

1. f(x)= 2 + x² b) f(x)= 5x + x³ + 2

1. For f(x) = -2 – x and g(x) = 2x² – 2x + 5, find g(f(-x)) , f(g(x\2)).

2. What is the largest domain for which f(x) has an inverse function?

1. y= b) y= x² – 8x + 16

1. Write f(x) = | 3x | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

12-variant

1. For f(x) = x – 3x² +1 , find f(0) , f( 3x - 4) , f(1\2x) and f( x\2) .

2. For f(x) = 12 –4x² and g(x) = x + 2, find g(f(-5x)) , f(g(x\10)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – x b) y=

1. Sketch the graph of y= | 1 - x² |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same

13-variant

1. For f(x) = 3x² – x + 3 , find f(3) , f( -x-3) , f(2\x) and f( x\2) .

2. For f(x) = x² + 1 and g(x) = x² – 1 , find g(f(x)) , f(g(x)).

3. For each function f(x), find the inverse function f^-1(x).

a) y= 2x+2 b) y=

1. Sketch the graph of y= x² + 4x .

2. (Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

14-variant

1. For the following functions, find f ( 5 ).

1. f(x)= x⁴+ x² + 2 b) f(x)= 2 + 2x² - x³

1. For f(x) = 2 + x and g(x) = 2x² – 5x + 2, find g(f(x)) , f(g(2)).

2. What is the largest domain for which f(x) has an inverse function?

1. y= b) y= x² – x

1. Write f(x) = | 2x +1 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

15-variant

1. For f(x) = – 3x² + 1 , find f(3) , f( 3x +2) , f(1\x) and f( x\2) .

2. For f(x) = 2x² -1 and g(x) = 2x² + 1, find g(f(x)) , f(g(2\x)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – 2x + 2 b) y=

1. Sketch the graph of y= | x + 1 |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

16-variant

1. For f(x) = x² + 5x – 3 , find f(4) , f( 2x-1) , f(2\x) and f( x\5) .

2. For f(x) = 3x+1 and g(x) = x² + 7x – 3 , find g(f(x)) , f(g(x)).

3. For each function f(x), find the inverse function f^-1(x).

a)y= 5x+2 b) y= c) y= x² + 6x + 6

1. Sketch the graph of y= x² + 2x – 8.

2. (Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

17-variant

1. For the following functions, find f (-2).

1. f(x)= 2 - 3x² b) f(x)=1+ 5x - x³

1. For f(x) = 2 – 5x and g(x) = 2x² – x + 5, find g(f(2x)) , f(g(-1))

2. What is the largest domain for which f(x) has an inverse function?

3. y= b) y= x² – 2x

Write f(x) = | x – 3 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

18-variant

1. For f(x) = 10 + x – 3x² , find f(-1) , f( x - 4) , f(1\3x) and f( x\2) .

2. For f(x) = 2 – x² and g(x) = 2x + 5, find g(f(-x)) , f(g(x\3)).

3. For each function f(x), find the inverse function f^-1(x).

a)y= x² – 4x b) y=

4. Sketch the graph of y= | 4x – 1 |.

5.( Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

19-variant

1.For f(x) = 3x² – 1 , find f(-2) , f( -x-1) , f(2\3x) and f( 2x\5) .

2.For f(x) = x+1 and g(x) = x² + x , find g(f(x)) , f(g(x)). 3. For each function f(x), find the inverse function f^-1(x).

a) y= x+2 b) y= c) y= -x² + 6x

4.Sketch the graph of y= x² + 4x +3.

5. (Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

20-variant

1.For the following functions, find f ( 5 ).

a) f(x)= 2 + x² b) f(x)=11 - x - 2x³

2.For f(x) = 1 + x and g(x) = 2x² – 5x + 2, find g(f(x)) , f(g(0)).

3.What is the largest domain for which f(x) has an inverse function?

a) y= b) y= 2x² – 1

1. Write f(x) = | x +1 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

21-variant

1. For f(x) = x – 3x² , find f(1) , f( x +2) , f(1\x) and f( -3x\2) .

2. For f(x) = 2x² -1 and g(x) = 2x - 1, find g(f(3x)) , f(g(2\x)).

3. For each function f(x), find the inverse function f^-1(x).

a)y= x² – 4x + 4 b) y=

1. Sketch the graph of y= | x – 1 |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

22-variant

1. For f(x) = 10 – 3x² , find f(-3) , f( 4x - 3) , f(3\x) and f( x\2) .

2. For f(x) = 2 + x² and g(x) = x(x + 5) + 1, find g(f(-x)) , f(g(x\3)).

3. For each function f(x), find the inverse function f^-1(x).

a)y= x² – 4x + 4 b) y=

4. Sketch the graph of y= | x + 1 |.

5. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

23-variant

1.For the following functions, find f (-1).

a) f(x)= 2 + x + 3x² b) f(x)=1 + 5x² - x³

2. For f(x) = 1 + x and g(x) = 2x² – x + 5, find g(f(7x)) , f(g(-7)).

3. What is the largest domain for which f(x) has an inverse function?

a) y= b) y= 2x² – 4x + 2

4. Write f(x) = | 3x – 1 | as piecewise function.

5. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential

24- variant

1.For f(x) = 1 +x² – x³ , find f(0) , f( x - 3) , f(1\x) and f( -x\2) .

2.For f(x) = 12 + x² and g(x) = 3(x + 5) + 1, find g(f(-x)) , f(g(1\3)).

3.For each function f(x), find the inverse function f^-1(x).

1. y= x² – 6x + 10 b) y=

4. Write f(x) = as piecewise function.

5.Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.

25-variant

1. For f(x) = 2x² + x – 3 , find f(-x) , f( 2x-1) , f(1\x) and f( x\2) .

2. For f(x) = -2x+1 and g(x) = -x² + 7x , find g(f(x)) , f(g(x)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= -x+2 b) y=

4. Sketch the graph of y= x² + 2x – 3.

5.(Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

26-variant

1. For the following functions, find f (-3).

1. f(x)= 2 + x² b) f(x)= 5x + x³ + 2

2.For f(x) = -2 – x and g(x) = 2x² – 2x + 5, find g(f(-x)) , f(g(x\2)).

3. What is the largest domain for which f(x) has an inverse function?

1. y= b) y= x² – 8x + 16

1. Write f(x) = | 3x | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

27-variant

1. For f(x) = x – 3x² +1 , find f(0) , f( 3x - 4) , f(1\2x) and f( x\2) .

2. For f(x) = 12 –4x² and g(x) = x + 2, find g(f(-5x)) , f(g(x\10)).

3. For each function f(x), find the inverse function f^-1(x).

1. y= x² – x b) y=

1. Sketch the graph of y= | 1 - x² |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same

28-variant

1.For f(x) = 3x² – x + 3 , find f(3) , f( -x-3) , f(2\x) and f( x\2) .

2.For f(x) = x² + 1 and g(x) = x² – 1 , find g(f(x)) , f(g(x)).

3.For each function f(x), find the inverse function f^-1(x).

a) y= 2x+2 b) y=

4.Sketch the graph of y= x² + 4x .

5.(Tarjima qiling) Domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, increase, same, similar, alteration, exponential, special, average, doubled, arbitrary, summary, formulas reduced multiplication, assumption, comparison, length, asymptote, reciprocal

29-variant

1. For the following functions, find f ( 5 ).

a) f(x)= x⁴+ x² + 2 b) f(x)= 2 + 2x² - x³

1. For f(x) = 2 + x and g(x) = 2x² – 5x + 2, find g(f(x)) , f(g(2)).

2. What is the largest domain for which f(x) has an inverse function?

y= b) y= x² – x

1. Write f(x) = | 2x +1 | as piecewise function.

1. (Tarjima qiling) Absolute value, axis, inverse function, defined, connection, above limit, lower limit, disposition, monotone, reduction, increase, special, body, average, doubled, proper, arbitrary, constant, important , summary, composite function, related, fraction, exponential.

30-variant

1. For f(x) = – 3x² + 1 , find f(3) , f( 3x +2) , f(1\x) and f( x\2) .

2. For f(x) = 2x² -1 and g(x) = 2x² + 1, find g(f(x)) , f(g(2\x)).

3. For each function f(x), find the inverse function f^-1(x).

a)y= x² – 2x + 2 b) y=

1. Sketch the graph of y= | x + 1 |.

2. (Tarjima qiling) Composite, graph, range, disposition, monotone, reduction, increase, domain, graph, range, pattern, restrict, reflection, decrease, belong, initial, arbitrary, constant, important , summary, formulas reduced multiplication, exponential, special, average, doubled, same.