Third graphrepresents the function
over the interval ![\left[ { - 3,3} \right].](https://tex.z-dn.net/?f=%5Cleft%5B%20%7B%20-%203%2C3%7D%20%5Cright%5D.)
Further explanation:
Given:
The function is ![f\left( x \right) = \left\lfloor x \right\rfloor- 2.](https://tex.z-dn.net/?f=f%5Cleft%28%20x%20%5Cright%29%20%3D%20%5Cleft%5Clfloor%20x%20%5Cright%5Crfloor-%202.)
The function is defined in the interval ![\left[ {-3,3}\right].](https://tex.z-dn.net/?f=%5Cleft%5B%20%7B-3%2C3%7D%5Cright%5D.)
Explanation:
The greatest integer function is represented ![y = \left\lfloor x \right\rfloor.](https://tex.z-dn.net/?f=y%20%3D%20%5Cleft%5Clfloor%20x%20%5Cright%5Crfloor.)
The greatest integer can also be known as floor function. The function is integral part of real numbers.
The values of greatest function
in interval
can be obtained as follows,
Substitute
for
in the function ![f\left( x \right)= \left\lfloor x \right\rfloor- 2.](https://tex.z-dn.net/?f=f%5Cleft%28%20x%20%5Cright%29%3D%20%5Cleft%5Clfloor%20x%20%5Cright%5Crfloor-%202.)
![\begin{aligned}f\left({- 3} \right)&=\left\lfloor{ - 3} \right\rfloor- 2\\&=- 3- 2\\&=- 5\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%5Cleft%28%7B-%203%7D%20%5Cright%29%26%3D%5Cleft%5Clfloor%7B%20-%203%7D%20%5Cright%5Crfloor-%202%5C%5C%26%3D-%203-%202%5C%5C%26%3D-%205%5C%5C%5Cend%7Baligned%7D)
Substitute
for
in the function ![f\left( x \right)=\left\lfloor x \right\rfloor- 2.](https://tex.z-dn.net/?f=f%5Cleft%28%20x%20%5Cright%29%3D%5Cleft%5Clfloor%20x%20%5Cright%5Crfloor-%202.)
![\begin{aligned}f\left( 3 \right)&= \left\lfloor3\right\rfloor- 2\\&=3- 2\\&=1\\\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Df%5Cleft%28%203%20%5Cright%29%26%3D%20%5Cleft%5Clfloor3%5Cright%5Crfloor-%202%5C%5C%26%3D3-%202%5C%5C%26%3D1%5C%5C%5Cend%7Baligned%7D)
The minimum value of the function in ![\left[ { - 3,3} \right] {\text{is}\: \boxed{ - 5}.](https://tex.z-dn.net/?f=%5Cleft%5B%20%7B%20-%203%2C3%7D%20%5Cright%5D%20%7B%5Ctext%7Bis%7D%5C%3A%20%5Cboxed%7B%20-%205%7D.)
The maximum value of the function in ![\left[ { - 3,3} \right] {\text{is}\: \boxed{1}.](https://tex.z-dn.net/?f=%5Cleft%5B%20%7B%20-%203%2C3%7D%20%5Cright%5D%20%7B%5Ctext%7Bis%7D%5C%3A%20%5Cboxed%7B1%7D.)
Third graphrepresents the function
over the interval ![\left[{ - 3,3}\right].](https://tex.z-dn.net/?f=%5Cleft%5B%7B%20-%203%2C3%7D%5Cright%5D.)
Kindly refer to the image attached.
Learn more
1. Learn more about the polynomial brainly.com/question/12996944
2. Learn more about logarithm model brainly.com/question/13005829
3. Learn more about the product of binomial and trinomial brainly.com/question/1394854
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.