We can't graph anything on this forum (yet)...) to determine whether it goes right through or only touches.A polynomial function is a mathematical function that can be written in the form f(x) = anxn + an-1xn-1 + ... + a1x + a0, where an through a0 are constants and x is the variable. It is a type of algebraic function that involves powers and coefficients of a variable.
To graph a polynomial function, you can plot several points on the coordinate plane by substituting different values for x in the function and solving for y. You can also use the leading coefficient, degree, and end behavior of the function to determine the general shape of the graph. Once you have plotted enough points, you can connect them with a smooth curve to create the graph of the polynomial function.
An x-intercept is a point on the graph of a function where the graph crosses or touches the x-axis. It is the value of x at which the function has a y-value of 0. In other words, it is a value of x that makes the function equal to 0. On a graph, x-intercepts are represented by points on the x-axis.
To find the x-intercepts of a polynomial function, you can set the function equal to 0 and solve for x. This will give you the x-values at which the function crosses the x-axis. You can also use a graphing calculator or software to find the x-intercepts by graphing the function and looking for the points where the graph crosses the x-axis.
X-intercepts are important for polynomial functions because they give us information about the roots or solutions of the function. They can help us determine the number of real solutions to an equation, the behavior of the graph, and the domain and range of the function. Additionally, x-intercepts can be used to find the factors of a polynomial function, which is useful for solving equations or simplifying expressions.