Chapter One: Precalculus Review

Question 1

function

Answer 1

a relationship between two sets that pairs one object in the first set with one and only one object in the second set

Question 2

slope-intercept form

Answer 2

y = mx + b

Question 3

slope formula

Answer 3

Question 4

point-slope form

Answer 4

(y - y₁) = m(x - x₁)

Question 5

parabola

Answer 5

consists of the set of all points in a plane that are equidistant from a fixed line (the directrix) and a fixed point not on the line (the focus)

Question 6

pythagorean theorem

Answer 6

a² + b² = c²

Question 7

distance formula

Answer 7

Question 8

exponential function

Answer 8

expressed as f(x) = N^x, where N>0

Question 9

definition of inverse functions

Answer 9

if f(g)(x) = x and g(f)(x) = x for all the x domain, then f and g are inverse functions

Question 10

inverse functions are a reflection over the line

Answer 10

y = x

Question 11

which types of functions have an inverse?

Answer 11

one-to-one functions, or those that pass the horizontal and vertical line tests

Question 12

a graph must pass what test to be a function?

Answer 12

the vertical line test

Question 13

properties of logs

Answer 13

• log_bb^a = a
• b^log_ba = a
• log_b(ac) = log_ba + log_bc
• log_b(a^c) = clog_ba
• log_b(a/c) = log_ba - log_bc
• change of base: log_bx = (log_ax)/(log_ab)