A table, a cubic and a model type…

Name: ______________________ Date: ____________ A table, a cubic and a model type justified (6 points)

Table

The table gives values of the increasing function

f

at selected values of

x

. The function

g

is given by

g(x) = x^3 - 6x^2 + 9x + 2

Selected values of the function f
$x$	0	2	4	6	8
$f(x)$	3	4.8	7.68	12.288	19.6608

(A(i)) Find the average rate of change of $f$ over the interval $0 \le x \le 4$ and over the interval $4 \le x \le 8$ . [1 point]
(A(ii)) Based on the results of part A(i), is the graph of $f$ concave up or concave down on $0 \le x \le 8$ ? Give a reason for your answer. [1 point]
(B(i)) Solve $g(x) = 4$ for all values of $x$ . Give your answers correct to three decimal places where needed. [1 point]
(B(ii)) Express the end behavior of $g$ , as $x$ decreases without bound and as $x$ increases without bound, using the mathematical notation of limits. [1 point]
(C(i)) Is a linear function or an exponential function a better model for the values in the table? Justify your answer, using the input and output values in the table. [1 point]
(C(ii)) Write an expression for an exponential function that matches every value in the table. [1 point]

A table, a cubic and a model type justified