### Home > APCALC > Chapter 3 > Lesson 3.1.1 > Problem3-15

3-15.

Recall the conjecture you developed in problem 3-5 and use it to determine the slope function, $f^\prime$, for each of the following functions.

1. $f(x) = x^9$

BASIC CONJECTURE that you should have made during class:The slope function is one-degree lower than the original function.

ADVANCED CONJECTURE that you might have made during class:The slope function is one degree lower than the original function AND stretched by the degree of the original function.

slope function $=9x^8$

1. $f(x) = x^{13}$

Refer to hint for part (a).

1. $f(x) = 2x$

This one does not require a conjecture - an Algebra I student could do it! This is the equation of a straight line. What is its slope?

1. $f(x) = 6$

Refer to hint for part (c).