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What are some reasons that you might have a nonzero y-intercept on a graph?
For any relationship between x and y, the value of y at x=0 (the y intercept) could be anything depending on what the relationship is. What was your weight when you were born? There are infinitely more relationships that are nonzero when x=0, than are zero.
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".
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.
Can a graph of a polynomial function have no y-intercept?
Yes. A lot of hyperbolic functions have no y- intercept. Also functions of the form Y=1/x^n Will only go to positive infinity as it approaches zero from the positive x direction and go to negative infinity as it approaches zero from the negative x direction. * * * * * While all that is true, the functions mentioned in the above answer are not polynomial functions! All polynomial functions will have a y-intercept provided there is no additional restriction on the domain so as to exclude x = 0.
Why does the constant term of a polynomial written in standard form give you the y intercept of the graph?
In a polynomial written in standard form, the constant term is the value of the polynomial when the input variable (usually (x)) is zero. This means that when you set (x = 0), the polynomial evaluates to the constant term, which corresponds to the point where the graph intersects the y-axis. Therefore, the constant term directly represents the y-intercept of the graph.
What would the meaning of a nonzero y - intercept to a graph of total mass versus volume?
Technically, a non-zero y-intercept can't exist in such a graph. If you were looking at such a graph, it was probably because they cut it short, and were just showing part of it.
What is the y-intercept of y equals 4x?
zero x-intercept also zero
What is y intercept and x intercept of y x plus 8?
To find the y intercept put zero in for x and solve. To find the x intercept put zero in for y and solve. (0,8) and (-8,0)
What is the 5 percent rule to find if the y-intercept is significant?
The 5 percent rule states that if a confidence interval for the y-intercept does not contain zero, then the y-intercept is considered statistically significant at the 5% level. This means that the y-intercept is unlikely to be zero in the population.
What is the slope and y-intercept and x-intercept of y equals -7?
Slope is zero y-intercept is -7 there is no x-intercept for this equation
How do you find the y interecepts for polynomial functions?
You set x = 0 and evaluate the polynomial. Note that this should be "y-intercept" in the singular, not in the plural.
What if the fourth derivative of a polynomial is zero?
There are many things that can be said about a polynomial function if its fourth derivative is zero, but the main thing you can know about this function from this information is that its order is 3 or less. Consider an nth order polynomial with only positive exponents: axn + bxn-1 + ... + cx2 + dx + e As you derive this function, its derivatives will eventually be equal to zero. The number of derivatives that are nonzero before they all become zero can tell you what order the polynomial function was. Consider an example, y = x4. y = x4 y' = 4x3 y'' = 12x2 y''' = 24x y(4) = 24 y(5) = 0 The original polynomial was of order 4, and its derivatives were nonzero up until its fifth derivative. From this, you can generalize to say that any function whose fifth derivative is equal to zero is of order 4 or less. If the function was of higher order than 4, its derivatives would not become zero until later. If the function was of lower order than 4, its fifth derivative would still be zero, but it would not be the first zero-valued derivative. So this experimentation yielded a rule that the first zero-valued derivative is one greater than the order of the polynomial. Your problem states that some polynomial has a fourth derivative that is zero. Our working rule states that this polynomial can be of highest order 3. So, your polynomial can be, at most, of the form: y = ax3 + bx2 + cx + d Letting the constants a through d be any real number (including zero), this general form expresses any polynomial that will satisfy your condition.
