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katrin2010 [14]
4 years ago
5

State the domain and range for: y= √ x - 3+6

Mathematics
1 answer:
Elenna [48]4 years ago
8 0

Answer:

D = {x|x∈R|x≥3}

R = {y|y∈R|y≥6}

Step-by-step explanation:

y = √(x - 3) +6

This graph type is a root graph because y = √ of something. Root graphs have a vertex point that none of the "x" and "y" values pass.

The vertex is (3, 6). Inside the root, - 3, represents the negative x value of the vertex. The x value is 3 because the inside of a root cannot equal to less than 0. If x was 3, √(x - 3) is √0. If x was 4, √(x - 3) is √(-1), an imaginary number.

The number outside of the root is the y coordinate. + 6

Since there is no negative outside the root, like -√(x - 3), the root continues to the upward, so "y" has to be greater than the y-coordinate in the vertex.

The graph continues rightward because the root is not imaginary, so x has to be greater than the x-coordinate in the vertex. An imaginary root like √-(x - 3) continues leftward.

Both "x" and "y" can also be any number, decimal or whole, so it's a real number, represented by R.

D = {x|x∈R|x≥3}

R = {y|y∈R|y≥6}

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Assuming you have a graphing calculator or a program to lets you graph equations (I use desmos) you simply put in the equetions and note down the coordinates of the point of intersection.

In the graph the first equation is in blue and the second in red.

The point of intersection = the solution = (-6 , -1)



If you dont have access to a graphing calculator you could draw the graphs by hand;

1) Draw a table of values for each equation; you do this by setting three or four values for x and calculating its image in y (you can use any values of x)

y = 0.5 x + 2 (Im writing 0.5 instead of 1/2 because I find its easier in this format)

x | y
-1 | 1.5 * y = 0.5 (-1) + 2 = 1.5
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y = x + 5

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2) Plot these point on the graph
I suggest to use diffrent colored points or diffrent kinds of point markers (an x or a dot) to avoid confusion about which point belongs to which graph

3) Using a ruler draw a line connection all the dots of one graph and do the same for the other

4) The point of intersection is the solution

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Answer:

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The relationship between the number of cups of water and sugar in this recipe is given as;

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