AP Precalculus FRQ: A doubling table

Question 1, Function Concepts (graphing calculator), 6 pointsAbout 18 minutes · Graphing calculator

A table with a row of x values 0, 1, 2, 3, 4 and a row of f(x) values 3, 6, 12, 24, 48.
$x$	0	1	2	3	4
$f(x)$	3	6	12	24	48

Let

f

be an increasing function defined for all real numbers. The table gives values of

f(x)

at selected values of

x

. The function

g

is given by

g(x)

= \dfrac{2x^2 - 8}{x^2 + x - 6}

(A) (i) Find the value of

(g \circ f)(1)

, or indicate that it is not defined. (ii) Find the value of

f^{-1}(12)

, or indicate that it is not defined. 2 points

(B) (i) The graph of

g

has a hole. Find the coordinates of the hole. (ii) Determine the end behavior of

g

x

increases without bound. Express your answer using the mathematical notation of a limit. 2 points

f

: linear, quadratic or exponential? (ii) Give a reason for your answer in part C (i) based on the relationship between the change in the output values of

f

and the change in the input values of

f

. Refer to the values in the table in your reasoning. 2 points

A doubling table and a rational function