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Ivanshal [37]
2 years ago
5

Someone please help. Ill give you brainiest.

Mathematics
1 answer:
Dimas [21]2 years ago
8 0
19. The absolute value equation of the graph is: y — | x - 0 | + 2 where (0,2) is the vertex.

Domain: (-∞, ∞)
Range: (-∞, 2]

A function is a relation in which no two ordered pairs have the same first component (inputs/x-values/domain) and different second components (outputs/y-values/range).

In determining whether a given relation is a function, we need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)? 

In the case of an absolute value function, its relation is a function because each input corresponds to exactly one output. To demonstrate, I performed a Vertical Line test to show why it is a function.

The Vertical Line Test (VLT) allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. As the attached graph of the absolute value function, EACH vertical line drawn crosses the graph only once. This graph passes the VLT, making it a function.


20.)

The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.

The set of second components (y-coordinates) is the RANGE of the relation.

Domain: {-2, -1, 0, 1}.
Range: {4, 3, 2, 1, 0}.

The given relation is NOT a function. As you can see from the given diagram, the input value of 2 corresponds to two output values: 4 and 0.

Please mark my answers as the Brainliest if you find my explanation helpful :)

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What is the product? x^2-16/2x+8 multiplied by x^3-2x^2+x/x^2+3x-4
Contact [7]

Answer:

(x (x - 4) (x - 1))/(2 (x + 4))

Step-by-step explanation:

Simplify the following:

((x^2 - 16) (x^3 - 2 x^2 + x))/((2 x + 8) (x^2 + 3 x - 4))

The factors of -4 that sum to 3 are 4 and -1. So, x^2 + 3 x - 4 = (x + 4) (x - 1):

((x^2 - 16) (x^3 - 2 x^2 + x))/((x + 4) (x - 1) (2 x + 8))

Factor 2 out of 2 x + 8:

((x^2 - 16) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

x^2 - 16 = x^2 - 4^2:

((x^2 - 4^2) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):

((x - 4) (x + 4) (x^3 - 2 x^2 + x))/(2 (x + 4) (x + 4) (x - 1))

Factor x out of x^3 - 2 x^2 + x:

(x (x^2 - 2 x + 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

The factors of 1 that sum to -2 are -1 and -1. So, x^2 - 2 x + 1 = (x - 1) (x - 1):

(x (x - 1) (x - 1) (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

(x - 1) (x - 1) = (x - 1)^2:

(x (x - 1)^2 (x - 4) (x + 4))/(2 (x + 4) (x + 4) (x - 1))

((x - 4) (x + 4) x (x - 1)^2)/(2 (x + 4) (x + 4) (x - 1)) = (x + 4)/(x + 4)×((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)):

(x (x - 4) (x - 1)^2)/(2 (x + 4) (x - 1))

Cancel terms. ((x - 4) x (x - 1)^2)/(2 (x + 4) (x - 1)) = ((x - 4) x (x - 1)^(2 - 1))/(2 (x + 4)):

(x (x - 4) (x - 1)^(2 - 1))/(2 (x + 4))

2 - 1 = 1:

Answer: (x (x - 4) (x - 1))/(2 (x + 4))

5 0
3 years ago
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uysha [10]
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4 0
3 years ago
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Which value is closest to the perimeter of the window?
Daniel [21]

Answer:12.85 feet

Step-by-step explanation:

Since the diameter of the circle is 5ft, the perimeter of the full circle would be 5 times pi feet, or about 15.7 ft. However, since we're only look at a half circle, the perimeter of the half circle is half that or about 7.85 feet. The other part of the perimeter is the diameter itself, so we add 5ft, to get a total of 12.85 feet.

4 0
3 years ago
Find the inverse f(x)=x+5/3x-1<br><br> f^-1(x)=
Kipish [7]

Answer:

  • f^-1(x) = (3/8)(x +1) . . . . as written
  • f^-1(x) = (x +5)/(3x -1) . . . with appropriate parentheses

Step-by-step explanation:

The inverse function can be found by solving for y:

  x = f(y)

  x = y + 5/3y -1 . . . . . . . . . . y +(5/3)y -1 . . . per order of operations

  x+1 = 8/3y . . . . . . . . . . add 1

  (3/8)(x +1) = y . . . . . . . . multiply by 3/8

  f^-1(x) = (3/8)(x +1) . . . . . inverse of the function as written

_____

Perhaps you intend f(x) = (x+5)/(3x-1). The inverse is found the same way.

  x = (y +5)/(3y -1)

  x(3y -1) = y +5

  3xy -x = y +5 . . . . . eliminate parentheses

  3xy -y = x + 5 . . . . . add x-y

  y(3x -1) = x +5 . . . . . factor out y

  y = (x +5)/(3x -1) . . . divide by the coefficient of y

  f^-1(x) = (x +5)/(3x -1) . . . . inverse of rational function

7 0
3 years ago
My dog Wrigley weighs 67.094. My brothers dog Kobe, weighs 47.940. How much more does my dog Wrigley weigh?
Viktor [21]

Answer:

19.154 :)

Step-by-step explanation:

67.094

-47.940

--------------

19.154

8 0
3 years ago
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