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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.
What are the X-intercepts and y-intercepts of a linear function?
The X-intercepts of a linear function are the points where the graph intersects the X-axis, occurring when the output (y) is zero. Conversely, the Y-intercept is the point where the graph intersects the Y-axis, occurring when the input (x) is zero. These intercepts can be found by setting the respective variables to zero in the linear equation. For example, in the equation (y = mx + b), the Y-intercept is (b), and the X-intercept can be found by solving (0 = mx + b).
How many y intercepts does a sine function have?
One intercept of the y-axis and infinitely many of the x-axis.
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.
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.
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.
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).
What are the X-intercepts and y-intercepts of a linear function?
The X-intercepts of a linear function are the points where the graph intersects the X-axis, occurring when the output (y) is zero. Conversely, the Y-intercept is the point where the graph intersects the Y-axis, occurring when the input (x) is zero. These intercepts can be found by setting the respective variables to zero in the linear equation. For example, in the equation (y = mx + b), the Y-intercept is (b), and the X-intercept can be found by solving (0 = mx + b).
