Problem 19
Determine whether each equation or table represents a linear or nonlinear function. Explain. $$x y=-6$$
Problem 20
Determine whether each equation or table represents a linear or nonlinear function. Explain. $$\begin{array}{|c|c|} \hline x & y \\ \hline 9 & -2 \\ \hline 11 & -8 \\ \hline 13 & -14 \\ \hline 15 & -20 \\ \hline \end{array}$$
Problem 23
Determine whether each equation or table represents a linear or nonlinear function. Explain. $$\begin{array}{|c|c|} \hline x & y \\ \hline-10 & 20 \\ \hline-9 & 18 \\ \hline-8 & 16 \\ \hline-7 & 14 \\ \hline \end{array}$$
Problem 26
Graph each pair of equations on the same coordinate plane. Describe their similarities and differences. $$\begin{aligned} &y=x^{2}\\\ &y=3 x^{2} \end{aligned}$$
Problem 29
Simplify each expression. $$\left(x^{4}+3 x^{2}+2\right)+-3\left(x^{2}+1\right)$$
Problem 30
Solve each equation. $$30=6(-2 w+3)$$
Problem 31
Explain how algebra tiles can be used to add polynomials. Include a description of how algebra tiles represent like terms and zero pairs.
Problem 32
Write a polynomial and a monomial, each having a degree no greater than 1. What is their product?
Problem 33
Which equation represents a nonlinear function if \(a>1 ?\) F. \(y=a x\) G. \(y=\frac{x}{a}\) H. \(y=a^{x}\) J. \(y=a+x\)
Problem 38
Explain how to find the degree of a polynomial. Illustrate your explanation by creating a monomial that has a degree of 3 and a polynomial that has a degree of 3.