By the definition of continuity, since the limit and f(x) both exist and are equal (to 0) at each value of x, y=0 is continuous. This is true for any constant function.
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If: 3x+y = 4 and x+y = 0 Then: x = 2 and y = -2
y = -x2 + 1 This function describes a parabola that opens downward. To find the top of it's range, you need to find it's focal point. You can do that very easily by taking the derivative of the equation and solving it for 0: y = -x2 + 1 ∴ y' = -2x let y' = 0: 0 = -2x ∴ x = 0 Now you can calculate the y value at that point: y = -02 + 1 ∴ y = 1 So that function describes an upside down parabola whose peak is at the point {0, 1}. It's range then is: {y | y ∈ ℜ, y ≤ 1}
y = 4(2x) is an exponential function. Domain: (-∞, ∞) Range: (0, ∞) Horizontal asymptote: x-axis or y = 0 The graph cuts the y-axis at (0, 4)
The [ 2x + 1 ] represents a function of 'y' .
Get in function form. - 3X - Y = 4 - 1(- Y = 3X + 4) Y = - 3X - 4 ----------------------------solve for X and Y by the 0 out method - 3X - 4 = 0 - 3X = 4 X = - 4/3 --------------- Y = - 3(0) - 4 Y = - 4 -------------- Draw a line linking those points.