# Hotmath Practice Problems

Title:
Hotmath Algebra 2
Author:
Hotmath Team
Chapter:Polynomial FunctionsSection:Finite Differences and Modeling Data with Polynomials

Problem: 1

Show that the nth–order differences for the given function of degree n are nonzero and constant:

f(x) = –x3 + 4x2 – 3x – 4

Problem: 3

Show that the nth–order differences for the given function of degree n are nonzero and constant:

f(x) = 4x4 – 40x

Problem: 5

A formula for the nth triangular number is f(n) = 1/2(n2 + n).

Show that this function has constant second–order differences.

Problem: 7

What is the degree of a polynomial P(x) if, in the equation

y = P(x),

the y–values are all equal for the 11th set of differences of consecutive x–values, and not equal for the 10th set of differences?

Problem: 9

Determine if y is a polynomial function of x.

If the result is a polynomial, find the degree.

Problem: 11

Determine if y is a polynomial function of x

If the result is a polynomial, find the degree.

Problem: 13

Find the values of the first differences of the function defined by given data points and find the degree of the function.

Plot the data points and find an equation for the line passing through the plotted points.

Problem: 15

For the given pattern, find f(5) and f(6).

f(1) = 13 =1

f(2) = 13 + 23 = 9

f(3) = 13 + 23 + 33 = 36

f(4) = 13 + 23 + 33 + 43 = 100

Also find the degree of the polynomial f(n) using the Polynomial –Difference Theorem.

Problem: 17

Say whether the following data can be modeled by a polynomial function. If it is polynomial then find its degree.

Problem: 19

Determine the degree of the polynomial function that models the data given in the table below.

Find a formula for the polynomial function.

Problem: 21

Write the cubic function of the graph shown.

Problem: 23

Write a cubic function whose graph passes through the given points:

(2, 0), (4, 0), (–3, 0), (3, 2)

Problem: 25

Write a cubic function whose graph passes through the given points:

(4, 0), (1, 0), (–2, 0), (0, 8)