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Maths-

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Question

The table gives some values of x and the corresponding values of f(x) for polynomial function f. Which of the following could be the graph of f in the xy-plane, where y = f(x) ?

The correct answer is:

The functional value at x = -2 is -2
Each grid represents 2 units
We observe x = -2 & f(x) = -2 in options (C) & (D)
The functional value at x = 0 is 2
We observe x = 0 & f (x) = 2 in option (A) & (D)
Commonly, we have option (D). So, the correction is (D).

Related Questions to study

Bill is planning to drive 1,000 miles to visit his family. If he plans to drive 250 miles per day, which of the following represents the remaining distance d, in miles, that Bill will have to drive to reach his family after driving for n days?

Bill is planning to drive 1,000 miles to visit his family. If he plans to drive 250 miles per day, which of the following represents the remaining distance d, in miles, that Bill will have to drive to reach his family after driving for n days?

The number of positive integral solutions of the equation $open vertical bar table row cell y to the power of 3 end exponent plus 1 end cell cell y to the power of 2 end exponent z end cell cell y to the power of 2 end exponent x end cell row cell y z to the power of 2 end exponent end cell cell z to the power of 3 end exponent plus 1 end cell cell z to the power of 2 end exponent x end cell row cell y x to the power of 2 end exponent end cell cell X to the power of 2 end exponent Z end cell cell x to the power of 3 end exponent plus 1 end cell end table close vertical bar equals 11$ is

The number of positive integral solutions of the equation $open vertical bar table row cell y to the power of 3 end exponent plus 1 end cell cell y to the power of 2 end exponent z end cell cell y to the power of 2 end exponent x end cell row cell y z to the power of 2 end exponent end cell cell z to the power of 3 end exponent plus 1 end cell cell z to the power of 2 end exponent x end cell row cell y x to the power of 2 end exponent end cell cell X to the power of 2 end exponent Z end cell cell x to the power of 3 end exponent plus 1 end cell end table close vertical bar equals 11$ is

If $open vertical bar table row cell a blank b blank 1 end cell row cell b blank c blank 1 end cell row cell c blank a blank 1 end cell end table close vertical bar equals 2010 text andif end text open vertical bar table row cell c minus a end cell cell c minus b end cell cell a b end cell row cell a minus b end cell cell a minus c end cell cell b c end cell row cell b minus c end cell cell b minus a end cell cell c a end cell end table close vertical bar minus open vertical bar table row cell c minus a end cell cell c minus b end cell cell c to the power of 2 end exponent end cell row cell a minus b end cell cell a minus c end cell cell a to the power of 2 end exponent end cell row cell b minus c end cell cell b minus a end cell cell b to the power of 2 end exponent end cell end table close vertical bar equals p$ then the number of positive divisors of the number p is

If $open vertical bar table row cell a blank b blank 1 end cell row cell b blank c blank 1 end cell row cell c blank a blank 1 end cell end table close vertical bar equals 2010 text andif end text open vertical bar table row cell c minus a end cell cell c minus b end cell cell a b end cell row cell a minus b end cell cell a minus c end cell cell b c end cell row cell b minus c end cell cell b minus a end cell cell c a end cell end table close vertical bar minus open vertical bar table row cell c minus a end cell cell c minus b end cell cell c to the power of 2 end exponent end cell row cell a minus b end cell cell a minus c end cell cell a to the power of 2 end exponent end cell row cell b minus c end cell cell b minus a end cell cell b to the power of 2 end exponent end cell end table close vertical bar equals p$ then the number of positive divisors of the number p is

parallel

If $A open parentheses table row 1 3 4 row 3 cell negative 1 end cell 5 row cell negative 2 end cell 4 cell negative 3 end cell end table close parentheses equals open parentheses table row 3 cell negative 1 end cell 5 row 1 3 4 row cell plus 4 end cell cell negative 8 end cell 6 end table close parentheses$ then $A equals negative times$

If $A open parentheses table row 1 3 4 row 3 cell negative 1 end cell 5 row cell negative 2 end cell 4 cell negative 3 end cell end table close parentheses equals open parentheses table row 3 cell negative 1 end cell 5 row 1 3 4 row cell plus 4 end cell cell negative 8 end cell 6 end table close parentheses$ then $A equals negative times$

Matrix Ais given by $A equals open curly brackets table attributes columnalign left end attributes row 3 11 row 2 8 end table close curly brackets$ then the determinant of $A to the power of 2011 end exponent minus 5 A to the power of 2010 end exponent$ is

Matrix Ais given by $A equals open curly brackets table attributes columnalign left end attributes row 3 11 row 2 8 end table close curly brackets$ then the determinant of $A to the power of 2011 end exponent minus 5 A to the power of 2010 end exponent$ is

If $open vertical bar table row alpha beta row gamma cell negative alpha end cell end table close vertical bar$ is to be square root of a determinant of the two rowed unit matrix, then $alpha comma beta comma$ $gamma$ should satisfy the relation

If $open vertical bar table row alpha beta row gamma cell negative alpha end cell end table close vertical bar$ is to be square root of a determinant of the two rowed unit matrix, then $alpha comma beta comma$ $gamma$ should satisfy the relation

parallel

The curve $y equals a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus 5$ touches the $x$ ‐axis at P(-2,0) and cuts the y ‐axis at a point $Q left parenthesis O comma 5 right parenthesis$ where its gradient is 3 Then a+2b+c=-

The curve $y equals a x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus 5$ touches the $x$ ‐axis at P(-2,0) and cuts the y ‐axis at a point $Q left parenthesis O comma 5 right parenthesis$ where its gradient is 3 Then a+2b+c=-

The point(s) on the curve $y to the power of 3 end exponent plus 3 x to the power of 2 end exponent equals 12 y$ where the tangent is vertical is (are)

The point(s) on the curve $y to the power of 3 end exponent plus 3 x to the power of 2 end exponent equals 12 y$ where the tangent is vertical is (are)

If the normal to the curve y=f(x) at the point (3, 4) makes an angle $fraction numerator 3 pi over denominator 4 end fraction$ with the positive $x$ ‐axis then $f to the power of ’ end exponent left parenthesis 3 right parenthesis equals$

If the normal to the curve y=f(x) at the point (3, 4) makes an angle $fraction numerator 3 pi over denominator 4 end fraction$ with the positive $x$ ‐axis then $f to the power of ’ end exponent left parenthesis 3 right parenthesis equals$

parallel

Tangent drawn at any point to the curve $f left parenthesis x right parenthesis equals x to the power of 5 end exponent plus 3 x to the power of 3 end exponent plus 4 x plus 8$ always makes

Tangent drawn at any point to the curve $f left parenthesis x right parenthesis equals x to the power of 5 end exponent plus 3 x to the power of 3 end exponent plus 4 x plus 8$ always makes

The number of points in the rectangle $left curly bracket left parenthesis x comma y right parenthesis vertical line minus 12 less or equal than x less or equal than 12 a n d minus 3 less or equal than y less or equal than 3 right curly bracket$ which lie on the curve $y equals x plus blank s i n blank x$ and at which the tangent to the curve is parallel to the $x$ ‐axis is

The number of points in the rectangle $left curly bracket left parenthesis x comma y right parenthesis vertical line minus 12 less or equal than x less or equal than 12 a n d minus 3 less or equal than y less or equal than 3 right curly bracket$ which lie on the curve $y equals x plus blank s i n blank x$ and at which the tangent to the curve is parallel to the $x$ ‐axis is

The system of homogeneous equations $t x plus left parenthesis t plus 1 right parenthesis y plus left parenthesis t minus 1 right parenthesis z equals 0 comma left parenthesis t plus 1 right parenthesis x plus l y plus left parenthesis t plus 2 right parenthesis z equals 0 comma$ $left parenthesis t minus 1 right parenthesis x plus left parenthesis t plus 2 right parenthesis y plus l z equals 0$ has a non‐ trivial solution for

The system of homogeneous equations $t x plus left parenthesis t plus 1 right parenthesis y plus left parenthesis t minus 1 right parenthesis z equals 0 comma left parenthesis t plus 1 right parenthesis x plus l y plus left parenthesis t plus 2 right parenthesis z equals 0 comma$ $left parenthesis t minus 1 right parenthesis x plus left parenthesis t plus 2 right parenthesis y plus l z equals 0$ has a non‐ trivial solution for

parallel

If $D left parenthesis x right parenthesis equals open vertical bar table row cell x minus 2 end cell cell left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end cell cell x to the power of 3 end exponent end cell row cell x minus 1 end cell cell x to the power of 2 end exponent end cell cell left parenthesis x plus 1 right parenthesis to the power of 3 end exponent end cell row x cell left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x plus 2 right parenthesis to the power of 3 end exponent end cell end table close vertical bar$ , then coefficient of $x$ in D(x) is :

If $D left parenthesis x right parenthesis equals open vertical bar table row cell x minus 2 end cell cell left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end cell cell x to the power of 3 end exponent end cell row cell x minus 1 end cell cell x to the power of 2 end exponent end cell cell left parenthesis x plus 1 right parenthesis to the power of 3 end exponent end cell row x cell left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end cell cell left parenthesis x plus 2 right parenthesis to the power of 3 end exponent end cell end table close vertical bar$ , then coefficient of $x$ in D(x) is :

$fraction numerator d over denominator d x end fraction open parentheses fraction numerator 2 x minus 3 over denominator 3 x plus 1 end fraction close parentheses equals$

$fraction numerator d over denominator d x end fraction open parentheses fraction numerator 2 x minus 3 over denominator 3 x plus 1 end fraction close parentheses equals$

Below is the graph of g'(x), the derivative of g(x) several x-coordinates, labeled A-F are marked. List them in the following order :

1) The point where g(x) is smallest 2) The point where g(x) is largest 3) The point where g'(x) is smallest 4) The point where g'(x) is largest 5) The point where g''(x) is smallest 6) The point where g''(x) is greatest

Below is the graph of g'(x), the derivative of g(x) several x-coordinates, labeled A-F are marked. List them in the following order :

1) The point where g(x) is smallest 2) The point where g(x) is largest 3) The point where g'(x) is smallest 4) The point where g'(x) is largest 5) The point where g''(x) is smallest 6) The point where g''(x) is greatest

parallel

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