how do you graph a polynomial function such as f(x)= 1/10(x=3)(x-1)(x-4)?
I know that I need to fing the x intercepts, End Behaviors, and, the turning points but i cannot figure out how to even get thosee. Please help.
YOu get the zeroes by setting f(x)=0.
zeroes are at x=-3, 1, 4
What is f(x) at x= inf?
What is f(x) at x=-very large?
Sorry, I'm still confused. How do you get from f(x)=0 to -3, 1 and 4.
what are the steps needed to solve this?
when for example x= 4
then
f(x) = something * (4-4) = 0
To graph a polynomial function like f(x) = (1/10)(x-3)(x-1)(x-4), you can follow these steps:
1. Find the x-intercepts:
To find the x-intercepts, set f(x) equal to zero and solve for x. In this case, set (1/10)(x-3)(x-1)(x-4) = 0. Since the product of three factors equals zero, at least one of the factors must be zero. Solve each factor individually to find the x-values where the graph intersects the x-axis.
2. Determine the end behaviors:
The end behavior of a polynomial is determined by the leading term, which is the term with the highest exponent. In this case, the leading term is (1/10)(x^3). If the leading term has an even degree (3 is odd), the graph will approach the same sign at both ends. If the leading term has an odd degree, the graph will approach opposite signs at the ends.
3. Identify the turning points:
The turning points of a polynomial occur where the graph changes direction. To find the turning points, you need to determine the local maxima and minima. To do this, you can find the derivative of the function and set it equal to zero. Solve for x to get the x-value(s) where the turning points occur. Use the second derivative test to determine whether each turning point is a maximum or minimum.
Once you have the x-intercepts, end behaviors, and turning points, you can plot these points on a graph and connect them to form the graph of the polynomial function. Additionally, you can also consider the behavior of the function in between these key points using symmetry and the degree of the function to help sketch the overall shape of the graph.