Tag: graphs of the form y=ax^2+bx+c

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Questions Related to graphs of the form y=ax^2+bx+c

Multiple choice business maths functions and graphs graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

If f is even function and g is an odd function, then $f _og$ is ............function.

  1. Even

  2. Odd

  3. Neither even nor odd

  4. Either even
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$fog$ function is an even function


Let $f\left(x \right)$ is a even function and $g \left( - x \right)$ is odd function.
So, $f\left( {g\left( { - x} \right)} \right) = f\left( { - g\left( x \right)} \right) = even$

Multiple choice business maths functions and graphs graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

State the whether given statement is true or false
If $f\left( x \right) = \dfrac{{x + 1}}{{x - 1}},$ then $f\left( x \right) + f\left( {\dfrac{1}{x}} \right) = 0$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$f\left( x \right) = \dfrac{{x + 1}}{{x - 1}}$


$f\left( \dfrac 1 x \right) = \dfrac{{\dfrac1x + 1}}{{\dfrac1x- 1}}=\dfrac{1+x}{1-x}=-\dfrac{1+x}{x-1}$

Hence, $f(x)+f(\dfrac1x)=\dfrac{{x + 1}}{{x - 1}}-\dfrac{{x + 1}}{{x - 1}}=0$

Multiple choice physics measurements and uncertainties graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

 Years Production of Car P  Production of Car Q Production of Car R 
2001  76  59  28
2002  82  62  36
2003  65  47 42 
2004  70  54  31
2005  85  57  49
2006  80  68  38

Direction (1-2) : Study the following table which shows the production of three different types of cars over the years.
The difference between the total production of three cars in the year $2004$ and $2006$ is _____.

  1. $11$

  2. $43$

  3. $31$

  4. $28$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total production of cars In year $2004$
$= 70 + 54 + 31 = 155$
Total production of cars in year $2006$
$= 80 + 68 + 38 = 186$
Hence, difference between the total production of three cars in the year $2004$ and $2006$
$= 186- 155 = 31$

Multiple choice physics measurements and uncertainties graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

 Years Production of Car P  Production of Car Q Production of Car R 
2001  76  59  28
2002  82  62  36
2003  65  47 42 
2004  70  54  31
2005  85  57  49
2006  80  68  38

Direction (1-2) : Study the following table which shows the production of three different types of cars over the years.
The average production of which of the following types of cars was maximum?

  1. $Q$

  2. $P$

  3. $R$

  4. All are equal
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average production of Car $P$
$=$ $\dfrac {\text{Sum of production of Car P in each year}}{\text{Total number of years}}$
$=$ $\dfrac {76 + 82 + 65 + 70 + 85 + 80}{6}$ $=$ $\dfrac {458}{6}$ $= 76.33$
Average production of Car $Q$
$=$ $\dfrac {59 + 62 + 47 + 54 + 57 + 68}{6}$ $=$ $\dfrac {347}{6}$ $= 57.83$
Average production of Car $R$
$=$ $\dfrac {28 + 36 + 42 + 31 + 49 + 38}{6}$ $=$ $\dfrac {224}{6}$ $= 37.33$
Clearly, average production of Car $P$ is greater than Car $Q$ and Car $R$.
Hence, the average production of Car $P$ is maximum.

Multiple choice business maths sets, relations and functions graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

If $f:\,\left( {3,6} \right) \to \left( {1,3} \right)$ is a function defined by $f\left( x \right) = x - \left[ {\frac{x}{3}} \right],\,then\,{f^{ - 1}}\left( x \right) = $

  1. $x-1$

  2. $x+1$

  3. $x$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given f(x) = x - [x/3] for x in (3, 6). For x in (3, 6), x/3 is in (1, 2), so [x/3] = 1. Thus f(x) = x - 1. Solving y = x - 1 for x gives x = y + 1, so f^-1(x) = x + 1.

Multiple choice business maths sets, relations and functions graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

The tangents to the graph of the function  $y=f(x)$ at the point with abscissa $x=1$ forms an angle of $\pi/6$ and the point $x=2$ an angle of $\pi/3$ and at the point $x=3$ an angle of $\pi/4$. The value of 
$\displaystyle \int _{1}^{2}{f'(x)f''(x)dx}+\displaystyle \int _{2}^{3}{f''(x)dx}$

  1. $\dfrac{4\sqrt{3}-1}{3\sqrt{3}}$

  2. $\dfrac{3\sqrt{3}-1}{2}$

  3. $\dfrac{4-\sqrt{3}}{3}$

  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice business maths sets, relations and functions graphs of the form y=ax^2+bx+c some more types of functions functions and their graphs

The graph of the function $\cos x\cos x(x+2)-\cos^{2}(x+1)$ is  

  1. A straight line through $(0, -\sin^{2}1)$ with slope $2$.

  2. A straight line through $(0, 0)$

  3. A parabola with vertex $(1, -\sin^{2}1)$

  4. A straight line through $\left(\dfrac{\pi}{2},-\sin^{2}1\right)$ and parallel to the $x-axis$.
Reveal answer Fill a bubble to check yourself
A Correct answer