Given:
The graph of a parabola.
To find:
The domain, range and check whether it is a function or not.
Solution:
Domain: The set of x-values or input values is known as domain.
Range: The set of y-values or output values is known as range.
A relation is a function if their exist unique outputs for each input. In other words a graph is a relation if it pass the vertical line test.
Vertical line test: Each vertical line intersect the graph at most once.
The given function is defined for all real values of x which are greater than or equal to -3. So, the domain of the given graph is:
The given function values can be any real number. So, the range of the given graph is:
For x=0, we have two values of the function because the graph intercept the y-axis at two points.
Since the graph does not pass the vertical line test therefore the given graph is not a function.
Answer:
Step-by-step explanation:
Given:
Radius of circular mirror, r = 6x
Length of metal frame, l = 18x
Area of square, As = l^2
Area of square = 18x × 18x
= 324 x^2.
Area of circular mirror, Ac = pi × r^2
= π × (6x)^2
= 36π x^2.
The expression for the area of the frame is subtracting the mirror from the metal frame = As - Ac
= 324x^2 - 36πx^2
= 36x2 (9 - π).
Answer:
8
Step-by-step explanation:
Rewrite the boundary lines <em>y</em> = -1 - <em>x</em> and <em>y</em> = <em>x</em> - 1 as functions of <em>y </em>:
<em>y</em> = -1 - <em>x</em> ==> <em>x</em> = -1 - <em>y</em>
<em>y</em> = <em>x</em> - 1 ==> <em>x</em> = 1 + <em>y</em>
So if we let <em>x</em> range between these two lines, we need to let <em>y</em> vary between the point where these lines intersect, and the line <em>y</em> = 1.
This means the area is given by the integral,
The integral with respect to <em>x</em> is trivial:
For the remaining integral, integrate term-by-term to get
Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line <em>y</em> = 1 and (0, -1)), so its area is 1/2*4*2 = 4.
