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A function cannot be one to many.
Suppose y = tan(x)
Now, since tan(x) = tan(x + pi)
then tan(x + pi) = y
But that means arctan(y) can be x or x+pi
In order to prevent that sort of indeterminacy, the arctan function must be restricted to an interval of width pi.
Any interval of that width would do and it could have been restricted to the first and second quadrants, or even from -pi/4 to 3*pi/4. The problem there is that in the middle of that interval the tan function becomes infinite which means that arctan would have a discontinuity in the middle of its domain. A better option, then, is to restrict it to the first and fourth quarters. Then the asymptotic values occur at the ends of the domain, which leaves the function continuous within the whole of the open interval.
What else can I help you with?
Which circles lie completely within the fourth quadrant?
Circles that lie completely within the fourth quadrant of the Cartesian plane have their centers in the fourth quadrant and have a radius smaller than the distance from the center to the x-axis and y-axis. In other words, the circle's center coordinates (x, y) must both be positive, and the radius r must be less than both x and y. This ensures that the entire circle falls within the boundaries of the fourth quadrant.
What quadrants would a zero abscissa and a negative ordinate be in?
A point with a zero abscissa (x-coordinate) and a negative ordinate (y-coordinate) would lie in the fourth quadrant of the Cartesian coordinate system. In this quadrant, the x-coordinate is positive or zero, while the y-coordinate is negative. This means that the point would be to the right of the y-axis (positive x-direction) and below the x-axis (negative y-direction).
Find the average value of the function on the given interval fx equals 2x to the power of3 open parentheses 1 plus x squared closed to the fourth power?
You need to clarify the function AND provide an interval.
What is the word for three quarters of a circle?
The word for three quarters of a circle is "quadrant." A quadrant is a sector equal to one fourth of a circle, so three quadrants make up three quarters of a circle. Each quadrant measures 90 degrees, totaling 270 degrees for three quarters of a circle.
What is the antonym of fourth?
fourth
What are the names of the quadrants on a graph?
The names of the quadrants on a graph are: First quadrant Second quadrant Third quadrant Fourth quadrant
Is it possible for a line to pass through exactly two quadrants?
Yes, it is possible for a line to pass through exactly two quadrants. For instance, a line that has a positive slope can pass through the first and third quadrants if it extends from the second quadrant to the fourth. Similarly, a line with a negative slope can pass through the second and fourth quadrants. In both cases, the line does not intersect the axes in such a way that it enters all four quadrants.
Is it possible for a fourth degree function to have an inverse that is a function?
In order for a fourth degree function to have an inverse function, its domain must be restricted. Otherwise the inverse function will not pass the vertical-line test.Ex.f(x) = x^4 (x>0), the original functionf-1(x) = x ^ (1/4), the inverse
What can you sa about the coordinates of all points that lie on the line bisecting the second and the fourth quadrants?
They satisfy the equation x + y = 0
How many quadrants in the cartesian plane?
The Cartesian plane is divided into four quadrants. These quadrants are determined by the signs of the x and y coordinates: the first quadrant (positive x, positive y), the second quadrant (negative x, positive y), the third quadrant (negative x, negative y), and the fourth quadrant (positive x, negative y).
Function of fourth ventricle?
gay
How do you graph an inverse variation function?
To graph an inverse variation function, typically represented as ( y = \frac{k}{x} ) (where ( k ) is a constant), start by plotting key points based on values of ( x ) and calculating corresponding ( y ) values. The graph will consist of two distinct branches in the first and third quadrants (if ( k > 0 )) or in the second and fourth quadrants (if ( k < 0 )). As ( x ) approaches zero, the values of ( y ) will increase or decrease towards infinity, creating asymptotes along the axes. Finally, connect the points smoothly to form the hyperbolic shape characteristic of inverse variations.
What are the numbers of a quadrants?
In a Cartesian coordinate system, the plane is divided into four quadrants. The first quadrant (Quadrant I) is where both x and y coordinates are positive, the second quadrant (Quadrant II) has negative x and positive y values, the third quadrant (Quadrant III) has both coordinates negative, and the fourth quadrant (Quadrant IV) features positive x and negative y values. Quadrants are typically numbered counterclockwise, starting from the upper right.
Do x and y coordinates have opposite signs!?
Yes, x and y coordinates can have opposite signs. This occurs in the second and fourth quadrants of the Cartesian coordinate system. In the second quadrant, x is negative and y is positive, while in the fourth quadrant, x is positive and y is negative.
What degree does tan equals negative square root of 3?
The tangent function equals negative square root of 3 at angles of ( 240^\circ ) and ( 300^\circ ) in the unit circle, which correspond to ( \frac{4\pi}{3} ) and ( \frac{5\pi}{3} ) radians, respectively. These angles are located in the third and fourth quadrants, where tangent is negative.
What is a quartic?
A quartic is an algebraic equation or function of the fourth degree.
What Given the following function choose the graph with the two possible angles with the domain 0 360. cos?
To find the angles where ( \cos(\theta) ) has specific values within the domain of ( 0^\circ ) to ( 360^\circ ), you would typically identify the corresponding reference angle and then consider both the first and fourth quadrants for positive values, and the second and third quadrants for negative values. For example, if you are looking for ( \cos(\theta) = 0.5 ), the angles would be ( 60^\circ ) and ( 300^\circ ). If you provide a specific cosine value, I can give you the exact angles.
