91Ó°ÊÓ

\(a\) and \(b\) are positive numbers and \(a>b\). Which is larger, \(f(a)\) or \(f(b)\) ? $$ f(r)=\sqrt{\frac{12}{r}} $$

If \(z\) is proportional to a power of \(y\) and \(y\) is proportional to a power of \(x\), is \(z\) proportional to a power of \(x\) ?

\(a\) and \(b\) are positive numbers and \(a>b\). Which is larger, \(f(a)\) or \(f(b)\) ? $$ f(t)=-3 t^{2}\left(-2 t^{3}\right)^{5} $$

Plot the expressions \(x^{2} \cdot x^{3}, x^{5},\) and \(x^{6},\) on three separate graphs in the window \(-1

Without solving them, say whether the equations in Exercises \(27-42\) have (i) One positive solution (ii) One negative solution (iii) One solution at \(x=0\) (iv) Two solutions (v) \(\quad\) Three solutions (vi) No solution Give a reason for your answer. $$ x^{1 / 3}=2 $$

Plot the expressions \(-x^{4}\) and \((-x)^{4}\) on the same graph in the window \(-1

If \(z\) is proportional to a power of \(x\) and \(y\) is proportional to the same power of \(x\), is \(z+y\) proportional to a power of \(x ?\)

\(a\) and \(b\) are positive numbers and \(a>b\). Which is larger, \(f(a)\) or \(f(b)\) ? $$ f(v)=-5\left((-2 v)^{2}\right)^{3} $$

If \(z\) is proportional to a power of \(x\) and \(y\) is proportional to a power of \(x\), is \(z y\) proportional to a power of \(x\) ?

\(a\) and \(b\) are positive numbers and \(a>b\). Which is larger, \(f(a)\) or \(f(b)\) ? $$ f(x)=2 \sqrt[3]{x}+3 \sqrt[9]{x^{3}} $$