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To find the y-intercepts of a polynomial function, set the value of ( x ) to 0 and solve for ( y ). This involves substituting 0 into the polynomial equation and simplifying to find the corresponding ( y )-value. The y-intercept is the point where the graph of the function crosses the y-axis, represented as the coordinate (0, ( y )).
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Can the graph of a polynomial function have no y-intercept?
No, the graph of a polynomial function cannot have no y-intercept. A polynomial function is defined for all real numbers, and when you evaluate it at (x = 0), you get the y-intercept, which is the value of the function at that point. Thus, every polynomial function will intersect the y-axis at least once, ensuring it has a y-intercept.
For which values does the cosecent functions have x intercepts?
The cosecant function, being defined as 1÷sin(x), has no x intercepts. It has y intercepts at ±∞. (infinity and -infinity)
What is the difference of x intercept and y intercept?
The y-intercept is the value of the function when 'x' is zero. That is, it's the point at which the graph of the function intercepts (crosses) the y-axis. The x-intercept is the value of 'x' that makes the value of the function zero. That is, it's the point at which 'y' is zero, and the graph of the function intercepts the x-axis.
How many y intercepts does a sine function have?
One intercept of the y-axis and infinitely many of the x-axis.
Why the graph of a polynomial function with real coefficients must have a y-intercept but may have no x-intercept?
For a polynomial of the form y = p(x) (i.e., some polynomial function of x), having a y-intercept simply means that the polynomial is defined for x = 0 - and a polynomial is defined for any value of "x". As for the x-intercept: from left to right, a polynomial of even degree may come down, not quite reach zero, and then go back up again. A simple example is y = x2 + 1. Why is the situation for "x" and for "y" different? Well, the original equation is a polynomial in "x"; but if you solve for "x", you don't get a polynomial in "y".
How do you determine the x-intercepts of the polynomial function?
set the values of the y equal to zero
Is the number of y-intercepts for a polynomial determined by the degree of the polynomial?
no...
How do you find the numbers x-intercepts of function y equals 5x'2?
5x²=0 X=0 the function y=5x² only intercepts x when x = 0
Is it possible for the graph of a quadratic function to have two y-intercepts?
Yes. A quadratic function can have 0, 1, or 2 x-intercepts, and 0, 1, or 2 y-intercepts.
Is the x-intercepts the same thing as zeros?
Yes, the places where the graph of a polynomial intercepts the x-axis are zeros. The value of y at those places must be 0 for the polynomial to intersect the x axis.
What are the values at which the graph of a polynomial crosses the x-axis?
The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0
For which values does the cosecent functions have x intercepts?
The cosecant function, being defined as 1÷sin(x), has no x intercepts. It has y intercepts at ±∞. (infinity and -infinity)
What is the difference of x intercept and y intercept?
The y-intercept is the value of the function when 'x' is zero. That is, it's the point at which the graph of the function intercepts (crosses) the y-axis. The x-intercept is the value of 'x' that makes the value of the function zero. That is, it's the point at which 'y' is zero, and the graph of the function intercepts the x-axis.
Find the x and y intercepts of 3x-2y6?
Given the linear equation 3x - 2y^6 = 0, the x and y intercepts are found by replacing the x and y with 0. This gives the intercepts of x and y where both = 0.
In the case of a quadratic function what is the number of x and y intercepts the function may have?
The greatest possible number of intercepts is: 2 of one axis and 1 of the other axis.The smallest possible number of intercepts is: One of each axis.
How do you graph this function y equals 1 plus x plus 3?
You find the intercepts on the x and y axis: First, sub in x=0, giving you y=4. Then sub in y=0, giving you x=-4. So your intercepts are (0,4) and (-4,0). Plot these 2 points, and draw a line between them (you can do this since your function is a straight line, not a curve).
How many y intercepts does a sine function have?
One intercept of the y-axis and infinitely many of the x-axis.
