Question

Which graph represents the function over the interval [−3, 3]?

Answer 1

 In mathematics, the functions of the whole part are functions that take a real number and return a whole number, either by excess or by default.
 Function floor (or ground), that to each real number assigns the nearest whole number by defect, that is to say, the greater whole number equal or smaller than that real number.
 Let's evaluate the extremes of the interval
 x = -3
 g (-3) = floor (-3) -2 = -5
 x = 3
 g (3) = floor (3) -2 = 1
 Therefore, the graph that best corresponds to the function in the given interval is the attached graph.

Answer 2

Third graphrepresents the function $f\left( x \right) = \left\lfloor x \right\rfloor-2$ over the interval $\left[ { - 3,3} \right].$

Further explanation:

Given:

The function is $f\left( x \right) = \left\lfloor x \right\rfloor- 2.$

The function is defined in the interval $\left[ {-3,3}\right].$

Explanation:

The greatest integer function is represented $y = \left\lfloor x \right\rfloor.$

The greatest integer can also be known as floor function. The function is integral part of real numbers.

The values of greatest function $f\left( x \right)= \left\lfloorx \right\rfloor- 2$ in interval $\left[{ - 3,3}\right]$ can be obtained as follows,

Substitute $-3$ for $x$ in the function $f\left( x \right)= \left\lfloor x \right\rfloor- 2.$

$\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}$

Substitute $3$ for $x$ in the function $f\left( x \right)=\left\lfloor x \right\rfloor- 2.$

$\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}$

The minimum value of the function in $\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.$

The maximum value of the function in $\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.$

Third graphrepresents the function $f\left( x \right)=\left\lfloor x\right\rfloor- 2$ over the interval $\left[{ - 3,3}\right].$

Kindly refer to the image attached.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Number system

Keywords: factor, factorization, polynomial, quadratic, cubic, greatest common factor, groups, multiplication, product, identities, common factor, expression, terms, grouping.