- This is an assessment test.
- To draw maximum benefit, study the concepts for the topic concerned.
- Kindly take the tests in this series with a pre-defined schedule.

## Algebra: Functions Test-6

Start

Congratulations - you have completed

*Algebra: Functions Test-6*.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%% Your answers are highlighted below.

Question 1 |

x and y are non-zero real numbers

f (x, y) = + (x +y)

g (x, y) = (x +y)

If f(x, y) =g (x, y) then

f (x, y) = + (x +y)

^{0.5},if (x +y)^{0.5}is real otherwise = (x +y)^{2}g (x, y) = (x +y)

^{2}if (x + y)^{0.5}is real, otherwise =- (x +y)If f(x, y) =g (x, y) then

A | x=y |

B | x+y= 1 |

C | x+y=-2 |

D | Both b and c |

Question 1 Explanation:

Going through all the options

The value of x and y could be anything so cant be sure about the functions

In this case, f (x, y) = + (x +y)

In this case both are 1

So f(x, y) =g (x, y)

The value of x and y could be anything so cant be sure about the functions

In this case, f (x, y) = + (x +y)

^{0.5 }g (x, y) = (x +y)^{2}In this case both are 1

So f(x, y) =g (x, y)

Question 2 |

A | y=ax+b |

B | y=a+bx+cx ^{2} |

C | y=e ^{ax+b} |

D | None of these |

Question 2 Explanation:

(a) Can be eliminated as looking at the data we can conclude that there is no linear relation between x and y

(b) Using the various values of x and y we can create the following equations

4=a+b+c -----------(1)

6=a+2b+4c---------(2)

14=a+3b+9c--------(3)

22=a+4b+16c

32=a+5b+25c

44=a+6b+36c

We will find the values of a,b and c using the first 3 equations and will check if the values satisfy the other 3 equations

Using eq 1 and 2 we get

2=b+3c

Using 2 and 3 we get

8=b+5c

Solving we get c=3,b=-7 and a=8

The values of a, b and c satisfy all the equations to a large limit.

(c) As the exponential function grows more quickly for small positive values as compared to large values,

while quite the opposite is happening here. So can’t be a match

(b) Using the various values of x and y we can create the following equations

4=a+b+c -----------(1)

6=a+2b+4c---------(2)

14=a+3b+9c--------(3)

22=a+4b+16c

32=a+5b+25c

44=a+6b+36c

We will find the values of a,b and c using the first 3 equations and will check if the values satisfy the other 3 equations

Using eq 1 and 2 we get

2=b+3c

Using 2 and 3 we get

8=b+5c

Solving we get c=3,b=-7 and a=8

The values of a, b and c satisfy all the equations to a large limit.

(c) As the exponential function grows more quickly for small positive values as compared to large values,

while quite the opposite is happening here. So can’t be a match

Question 3 |

If f(0, y) = y + 1, and f(x + I, y) =f (x, f (x, y)). Then, what is the value of f(1,2) ?

A | 1 |

B | 2 |

C | 3 |

D | 4 |

Question 3 Explanation:

F(1,2)=f(0,3)
F(0,3)=4
So,f(1,2)=4

Question 4 |

Functions m and M are defined as follows:m (a, b, c) = min (a + b, c, a)M(a, b, c) = max (a + b, c, a)If a = - 2, b = - 3 and c = 2 what is the maximum between
$ \displaystyle \left[ \frac{m\text{ }\left( a,\text{ }b,\text{ }c \right)+M\text{ }\left( a,\text{ }b,\text{ }c \right)}{2} \right]and\left[ \frac{m\text{ }\left( a,\text{ }b,\text{ }c \right)\text{ }M\text{ }\left( a,\text{ }b,\text{ }c \right)}{2} \right]$

A | 3/2 |

B | 7/2 |

C | -3/2 |

D | -7/2 |

Question 4 Explanation:

[m (a, b, c)+M (a, b, c)]/2=-3/2
[m (a, b, c) –M (a, b, c)]/2=-7/2
Max of the 2 is -3/2 which is the answer

Question 5 |

Functions m and M are defined as follows:
m (a, b, c) = min (a + b, c, a)
M(a, b, c) = max (a + b, c, a)If a b, and c are negative, then what gives the minimum of a and b

A | m (a,b,c) |

B | –M (-a, a,-b) |

C | m (a+b, b,c) |

D | None of these |

Question 5 Explanation:

As all a,b and c are negative

(a) m (a,b,c)=min(a+b,c,a)

(b) –M (-a, a,-b)=-max(0,-b,-a)

(c) m (a+b, b,c)=min(a+2b,c,a+b)

(a) m (a,b,c)=min(a+b,c,a)

(b) –M (-a, a,-b)=-max(0,-b,-a)

(c) m (a+b, b,c)=min(a+2b,c,a+b)

Once you are finished, click the button below. Any items you have not completed will be marked incorrect. Get Results

There are 5 questions to complete.

← | List | → |

Return

Shaded items are complete.

1 | 2 | 3 | 4 | 5 |

End |

Return

You have completed

questions

question

Your score is

Correct

Wrong

Partial-Credit

You have not finished your quiz. If you leave this page, your progress will be lost.

Correct Answer

You Selected

Not Attempted

Final Score on Quiz

Attempted Questions Correct

Attempted Questions Wrong

Questions Not Attempted

Total Questions on Quiz

Question Details

Results

Date

Score

Hint

Time allowed

minutes

seconds

Time used

Answer Choice(s) Selected

Question Text

All done

Need more practice!

Keep trying!

Not bad!

Good work!

Perfect!