91Ó°ÊÓ

Decide whether each statement is true or false. If false, tell why. Since \(x-1\) is a factor of \(f(x)=x^{6}-x^{4}+2 x^{2}-2,\) we can conclude that \(f(1)=0\).

Write each formula as an English phrase using the word varies or proportional. \(C=2 \pi r,\) where \(C\) is the circumference of a circle of radius \(r\)?

Provide a short answer to each question. What is the domain of \(f(x)=\frac{1}{x} ?\) What is its range?

Decide whether each statement is true or false. If false, tell why. Since \(f(1)=0\) for \(f(x)=x^{6}-x^{4}+2 x^{2}-2,\) we can conclude that \(x-1\) is a factor of \(f(x)\).

Write each formula as an English phrase using the word varies or proportional. \(d=\frac{1}{5} s,\) where \(d\) is the approximate distance (in miles) from a storm, and \(s\) is the number of seconds between seeing lightning and hearing thunder?

Write each formula as an English phrase using the word varies or proportional. \(r=\frac{d}{t},\) where \(r\) is the speed when traveling \(d\) miles in \(t\) hours?

Decide whether each statement is true or false. If false, tell why. Since \(2+3 i\) is a zero of \(f(x)=x^{2}-4 x+13,\) we can conclude that \(2-3 i\) is also a zero.

Provide a short answer to each question. What is the equation of the vertical asymptote of the graph of \(y=\frac{1}{x-3}+2 ?\) of the horizontal asymptote?

Write each formula as an English phrase using the word varies or proportional. \(s=k x^{3},\) where \(s\) is the strength of a muscle that has length \(x\)?

Use the factor theorem and synthetic division to decide whether the second polynomial is a factor of the first. See Example 1 . $$x^{3}-5 x^{2}+3 x+1 ; x-1$$