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Question 144966: 1. (a) Is the graph of a circle a graph of a function? Yes or no
(b) Find the center and the radius of the circle represented by the equation
x2 + y2 + 10x – 4y – 7 = 0
2. Let g(x)= 9-x/6+x
(a) Find g(–1)
(b) Find g(t + 1) and simplify.
(c) Find the domain of the function
3.Consider the points (4, –1) and (7, 8).
(a) Find the midpoint of the line segment with the given endpoints.
(b) Find the distance between the points. Give an exact answer (simplified as much as possible), and also an approximation to three decimal places.
(c) Find the slope of the line passing through the two given points.
(d) Find the equation of the line passing through the two given points.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. (a) Is the graph of a circle a graph of a function? Yes or no
(b) Find the center and the radius of the circle represented by the equation
x^2 + y^2 + 10x – 4y – 7 = 0
x^2+10x+25 + y^2 -4y + 4 = 7+25+4
(x+5)^2 + (y-2)^2 = 36
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Center: (-5,2) ; radius = 6
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2. Let g(x)= 9-x/6+x
(a) Find g(–1)
g(-1) = (9 + 1)/(6-1) = 2
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(b) Find g(t + 1) and simplify.
g(t+1) = (9-(t+1))/(6+(t+1))
g(t+1) = (8-t)/(7+t)
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(c) Find the domain of the function
Let g(x)= 9-x/6+x
Domain: All Real Numbers except x=-6
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3.Consider the points (4, –1) and (7, 8).
(a) Find the midpoint of the line segment with the given endpoints.
x = (4+7)/2 = 11/2
y = (-1+8)/2 = 7/2
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(b) Find the distance between the points. Give an exact answer (simplified as much as possible), and also an approximation to three decimal places.
d = sqrt[(8--1)^2+(7-4)^2] = sqrt(117)
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(c) Find the slope of the line passing through the two given points
slope = (8--1)/(7-4) = 9/3 = 3
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(d) Find the equation of the line passing through the two given points.
8 = 3*7 + b
b = -13
EQUATION: y = 3x -13
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Cheers,
Stan H.
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