# Analyzing 2 Functions. Help Please!

first function: f(x)= x^3-3x^2-6x+8
2nd function: f(x)= x^4-10x^3+35x^2-50x+24

1)whats y intercepts
2)whats x intercepts (zeros)
3)turning points
4)table and graph with appropriate scales
5)intervals of increase/decrease after you determined turning points
6)end behavior
7)symmetry: odd or even

for numbers 1 and 2 i think you have to put the functions onto the graphing calculator and find the y and x intercepts. i did that and i got 8 for the y intercept, -2, 1, 4 for the x intercept of the first function. for the 2nd function i think the y intercept is 30 and the x intercept is 1, 2 , 3, 4. are those intercepts right? that is by far all i know about this whole problem. i know how to graph the functions but how do i make table? I need help on turning points, intervals, end behavior, and symmetry of both functions. thanks for helping.

SammyS
Staff Emeritus
Homework Helper
Gold Member
To find the y-intercept plug-in x = 0. (Your answer is incorrect for the second function.)

Do you know what a turning point is? Your graphing calculator should be able to help you find these.

Do you know what it means for a function to be increasing? ... decreasing?

eumyang
Homework Helper
first function: f(x)= x^3-3x^2-6x+8
2nd function: f(x)= x^4-10x^3+35x^2-50x+24

1)whats y intercepts
2)whats x intercepts (zeros)
3)turning points
4)table and graph with appropriate scales
5)intervals of increase/decrease after you determined turning points
6)end behavior
7)symmetry: odd or even
For #6, look up Leading Term Test for Polynomials.
For #7, are you supposed to find the symmetry by looking at the graph, or algebraically? If algebraically, this involves finding f(-x).

HallsofIvy