Lesson 2: Rational Equations, Functions, and Inequalities

Question 1

an equation involving rational expressions

Answer 1

rational equation

Question 2

an inequality involving rational expression

Answer 2

rational inequality

Question 3

a function of the form f(x) = p(x)/q(x) where p(x) and q(x) are polynomial functions and q(x) is not the zero function

Answer 3

rational function

Question 4

what makes an expression not a rational equation, function, or inequality

Answer 4

no variable in radical sign, no fractional exponent, no variable in exponent

Question 5

what is the formula for speed

Answer 5

s = d/t

Question 6

a rational function 𝑓(𝑥) = P(x)/Q(x) is all values of x that will not make
the 𝑄(𝑥) equal to zero.

Answer 6

domain

Question 7

are all the possible resulting values of the dependent variables after we have substituted the domain.

Answer 7

range

Question 8

how to find the domain of a rational function

Answer 8

set the denominator equal to zero and solve for x

e.g. x+2/x-2
x-2 ≠ 0
x ≠ 2

Question 9

how to find the range of a rational function

Answer 9

find the inverse of the function, find the domain of the inverse function, state the range

Question 10

a point where the graph of the
rational function intersects the x- or y-axis.

Answer 10

intercept

Question 11

to determine the x-interecept

Answer 11

y=0

Question 12

to determine the y-intercept

Answer 12

x=0

Question 13

are the values of x which make the function zero.

Answer 13

zeroes

Question 14

zeroes are also known as

Answer 14

x-intercepts, solutions, or roots of functions

Question 15

a line or curve to which a function’s graph draws closer
without touching it.

Answer 15

asymptote

Question 16

Functions cannot cross a ____ asymptote and they usually approach _____ asymptotes in their end behavior

Answer 16

vertical
horizontal

Question 17

if the graph
of f either increases or decreases without bound as the x-values approach a from
the right or left.

Answer 17

vertical asymptote

Question 18

if f(x) gets
closer to b as x increases or decreases without bound (x -> __)

Answer 18

horizontal asymptote

Question 19

If the degrees of the numerator (n) is less than the degrees of the denominator
(m), y = 0 is

Answer 19

x-intercepts

Question 20

n (degree of the numerator)
m (degree of the denominator)

m < n

Answer 20

y=0

Question 21

n (degree of the numerator)
m (degree of the denominator)

m > n

Answer 21

no horizontal asymptote

Question 22

n (degree of the numerator)
m (degree of the denominator)

m = n

Answer 22

y = a/b

a and b is the leading coefficient of the numerator and denominator.

Question 23

how do you find the vertical asymptote

Answer 23

set the denominator equal to 0 and solve for x

e.g. x-2/x+2
x+2≠0
x≠-2