Math test rational functions 10th grade

Question 1

vertical line test

Answer 1

used to tell if its a function (can only intersect once)

Question 2

adding composite functions

Answer 2

f(x)+g(x) or (f+g)(x)

add together and combine like terms

Question 3

multiplying composite functions

Answer 3

f(x) x g(x) or (f x g)(x)

multiply together and simplify

Question 4

dividing composite functions

Answer 4

f(x)/g(x) (f/g)(x)

divide and simplify

Question 5

subtracting composite functions

Answer 5

f(x)-g(x)

subtract and combine like terms

Question 6

(gof)(x)

Answer 6

put the f function into the x of the g function

Question 7

(fog)(x)

Answer 7

put the g function into the x of the f function

Question 8

properties of inverse functions

Answer 8

• fof-1 (x) = f-1of (x)
• the graph of inverse functions are symmetric with respect to the y=x line
• points are the same but reversed
• domain and range are swapped

Question 9

how to find inverse

Answer 9

write the function in x/y notation
switch x and y
solve for y
revert to function notation

Question 10

how to prevent a parabola from failing the horizontal line test

Answer 10

remove one of the branches by imposing a domain of x>0

Question 11

do quadratic functions have an inverse

Answer 11

have an inverse function only if the domain is restricted

Question 12

general function form

Answer 12

p(x)/q(x)
ax+b/cx+d

Question 13

what is the graph of a function called

Answer 13

a hyperbola

Question 14

asymptote

Answer 14

a line that a function approaches as one of its variables approaches a value of +/- infinity

Question 15

asymptote form

Answer 15

a/x-h + k

Question 16

how to find asymptotes from asymptote form

Answer 16

x=h is vertical asymptote
y=k is horizontal asymptote

Question 17

to to graph from asymptote form

Answer 17

graph 2 points on either side of the vertical asymptote (sketch asymptotes as dotted lines first)
choose a point and plug it into the equation to find the other variable

Question 18

how to find asymptotes from general form

Answer 18

to find vertical asymptote, set the denominator = 0
(-d/c)
to find horizontal asymptote, do a/c

Question 19

domain

Answer 19

vertical asymptote

Question 20

range

Answer 20

horizontal asymptote

Question 21

how to find x and y intercepts

Answer 21

set x=0 or y=0 and solve for the opposite variable

Question 22

how to graph from general form

Answer 22

• graph asymptotes
• make a table replacing x for y

Question 23

important thing to remember when graphing

Answer 23

label everything including points and asymptotes

Question 24

word problems regarding speed of current

Answer 24

make a table, upstream vs downstream. And then distance, speed, time.

Speed = distance +/- x
time = distance/speed
add together the upstream and downstream and have them equal the total time.

Question 25

word problems regarding concentration

Answer 25

initial amount + rate(time) 200 + 2t put the substance /over the water

Question 26

inverse variation

Answer 26

y = k/x slope = k y intercept is 0 always goes through origin when graphed

Question 27

direct variation

Answer 27

y = kx for a line that passes through the origin the slope = k y intercept is always zero

Question 28

when a problem has both inverse and direct do

Answer 28

z = k(x/y)

Question 29

horizontal line test

Answer 29

tells us if a function has an inverse

Question 30

(f + g)(2)

Answer 30

means that x is 2

Question 31

x and y intercepts of function

Answer 31

set y to zero and set x to zero

Question 32

graph from general form

Answer 32

find asymptotes label them replace x and solve for y plot points