91Ó°ÊÓ

Are the statements true or false? Give an explanation for your answer. The function \(f(x)=\sin \left(x^{2}\right)\) is periodic, with period \(2 \pi\)

Complete the following table with values for the functions \(f, g,\) and \(h,\) given that: (a) \(f\) is an even function. (b) \(g\) is an odd function. (c) \(h\) is the composition \(h(x)=g(f(x))\) $$\begin{array}{r|c|c|c}\hline x & f(x) & g(x) & h(x) \\\\\hline-3 & 0 & 0 & \\\\-2 & 2 & 2 & \\\\-1 & 2 & 2 & \\\0 & 0 & 0 & \\\1 & & & \\\2 & & & \\\3 & & & \\\\\hline\end{array}$$

In Problems \(64-71\), find a value of the constant \(k\) such that the limit exists. $$\lim _{x \rightarrow-\infty} \frac{e^{2 x}-5}{e^{k x}+3}$$

Which of the following functions has its domain identical with its range? (a) \( f(x)=x^{2}\) (b) \(g(x)=\sqrt{x}\) (c) \(h(x)=x^{3}\) (d) \(i(x)=|x|\)

In Problems \(64-71\), find a value of the constant \(k\) such that the limit exists. $$\lim _{x \rightarrow \infty} \frac{x^{3}-6}{x^{k}+3}$$

Are the statements true or false? Give an explanation for your answer. The function \(g(\theta)=e^{\sin \theta}\) is periodic.

Explain what is wrong with the statement. The graph of \(f(x)=-(x+1)^{3}\) is the graph of \(g(x)=\) \(-x^{3}\) shifted right by 1 unit.

In Problems \(64-71\), find a value of the constant \(k\) such that the limit exists. $$\lim _{x \rightarrow \infty} \frac{3^{k x}+6}{3^{2 x}+4}$$

Explain what is wrong with the statement. \(f(x)=3 x+5\) and \(g(x)=-3 x-5\) are inverse functions of each other.

In Problems \(64-71\), find a value of the constant \(k\) such that the limit exists. $$\lim _{x \rightarrow-\infty} \frac{3^{k x}+6}{3^{2 x}+4}$$