What is the range of the function f(x) = –2|x + 1|?
2 answers:
Answer:
Range all real numbers less than or equal to 0
( - ∞ , 0 ]
Step-by-step explanation:
For visual understanding a graph of the function is attached with the answer.
- For calculating the range of any modulus function you need to know that if modulus is there across any function then the output will be always positive.
For example: x has a range of ( - ∞ , + ∞ ) but |x| has a range of [ 0 , + ∞ ). Similarly range of |x + 1| is [ 0 , + ∞ ).
- If you multiply the modulus function with a negative sign then the output will always be negative.
For example: Range of |x| is [ 0 , + ∞ ) but range of -|x| is ( - ∞ , 0 ]. Similarly range of -|x + 1| is ( - ∞ , 0 ]
- Range in this case won't be affected on multiplying a positive constant with the modulus function.
Therefore the range of f(x) = -2|x + 1| will be ( - ∞ , 0 ].
(NOTE : <em>[a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.</em>
<em>(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.</em>
<em>(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.</em>
<em>[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.</em>
<em>{a,b} means only 'a' and 'b'.</em>
<em>{a,b] or (a,b} doesn't mean anything.</em> )
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Answer:
The missing dimension is 4 units.
Step-by-step explanation:
In the given prism,
Of all the surfaces,
There are three rectangular surfaces and two triangular surfaces
<h2>Analyzing areas of rectangular surfaces:</h2>1)The two rectangles with dimensions of 15 units and 5 units:
The area of each rectangle = Length of rectangle Breadth of rectangle
From the diagram,
Length of rectangle = 15 units,
Breadth of rectangle = 5 units.
Area of each rectangle = 15 5 ;
Area of each rectangle = 75 square units.
Sum of areas of the two rectangles = 2 75
Sum of areas of the two rectangles = 150 square units (equation 1)
2) The rectangle with the dimensions 15 units and 6 units:
The area of thus rectangle= Length of rectangle Breadth of rectangle
From the diagram,
Length of rectangle = 15 units,
Breadth of rectangle = 6 units.
Area of the rectangle = 15 6 ;
Area of the rectangle = 90 square units. (equation 2)
From equation 1 and equation 2,
Therefore sum of areas of all rectangles in the prism = 150 + 90
Sum of areas of rectangles = 240 square units.
We also know,
Total surface area of the prism = Sum of areas of triangles + Sum areas of rectangles
Given, Total surface area of prism = 264 square units.
Therefore from the formula,
Sum of areas of triangles = Total surface area - sum of areas of reactangles
Sum of areas of triangles = 264 - 240
Sum of areas of triangles = 24 square units. (equation 3)
Let the missing dimension be 'h units'
<h2>Calculating sum of areas of triangles:</h2>From diagram,both triangles are congruent,hence have the same area
Area of a triangle =
From diagram,
Base = 6 units,
Height = h units.
Area of a triangle = = 3h square units.
Sum of the areas of both triangles = 3h+3h = 6h square units.
Using equation 3, we get
6h = 24;
h =
Therefore,
h = 4 units.
Therefore,
The missing dimension is 4 units.