What is the zero of a function and how does it relate to the functions graph?
A zero of a function is a point at which the value of the function is zero. If you graph the function, it is a point at which the graph touches the x-axis.
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.
Linear function: No variable appears in the function to any power other than 1. A periodic input produces no new frequencies in the output. The function's first derivative is a number; second derivative is zero. The graph of the function is a straight line. Non-linear function: A variable appears in the function to a power other than 1. A periodic function at the input produces new frequencies in the output. The function's first derivative is…
The domain of a function encompasses all of the possible inputs of that function. On a Cartesian graph, this would be the x axis. For example, the function y = 2x has a domain of all values of x. The function y = x/2x has a domain of all values except zero, because 2 times zero is zero, which makes the function unsolvable.
The zero of a linear function in algebra is the value of the independent variable (x) when the value of the dependent variable (y) is zero. Linear functions that are horizontal do not have a zero because they never cross the x-axis. Algebraically, these functions have the form y = c, where c is a constant. All other linear functions have one zero.
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…