Question

for each table below, select whether the table represents a function that is increasing or decreasing, and whether the function is concave up or concave down.

\\(\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline 1 & 128 \\\\ \\hline 2 & 150 \\\\ \\hline 3 & 168 \\\\ \\hline 4 & 182 \\\\ \\hline 5 & 192 \\\\ \\hline 6 & 198 \\\\ \\hline \\end{array}$$

\\)

\\(f(x)\\) is select an answer select an answer

\\(\

$$\begin{array}{|c|c|} \\hline x & g(x) \\\\ \\hline 1 & 72 \\\\ \\hline 2 & 50 \\\\ \\hline 3 & 32 \\\\ \\hline 4 & 18 \\\\ \\hline 5 & 8 \\\\ \\hline 6 & 2 \\\\ \\hline \\end{array}$$

\\)

\\(g(x)\\) is select an answer select an answer

\\(\

$$\begin{array}{|c|c|} \\hline x & h(x) \\\\ \\hline 1 & 2 \\\\ \\hline 2 & 8 \\\\ \\hline 3 & 18 \\\\ \\hline 4 & 32 \\\\ \\hline 5 & 50 \\\\ \\hline 6 & 72 \\\\ \\hline \\end{array}$$

\\)

\\(h(x)\\) is select an answer select an answer

\\(\

$$\begin{array}{|c|c|} \\hline x & k(x) \\\\ \\hline 1 & 198 \\\\ \\hline 2 & 192 \\\\ \\hline 3 & 182 \\\\ \\hline 4 & 168 \\\\ \\hline 5 & 150 \\\\ \\hline 6 & 128 \\\\ \\hline \\end{array}$$

\\)

\\(k(x)\\) is select an answer select an answer

Explanation:

Analyze first differences and second differences for each function

$$
LATEXBLOCK0
$$

Answer:

Question 1

\(f(x)\) is increasing and concave down

Question 2

\(g(x)\) is decreasing and concave up

Question 3

\(h(x)\) is increasing and concave up

Question 4

\(k(x)\) is decreasing and concave down