Functions
Compositions
Trig
Mappings
assorted donuts
100
to be a function, each input should have how many outputs?
one
100
f(x) = x+ 5
g(x) = x - 1
f(g(2)) =
6
100
how do you find the tan of an angle?
opposite/adjacent
100
the number you put into the function (input) is called the ....
preimage
100
Using the vertical line test, which of these is a function?
the second one
200
f(x) = x2 + 10
f(5) =
35
200
f(x) = 12 - x
g(x) = x2
g(f(3)) =
81
200
what does SOH CAH TOA stand for?
sin: opposite/hypotenuse
cos: adjacent/hypotenuse
tan: opposite/adjacent
200
if you have the mapping
T ◦ S : (4, 1)
which function would you do first, T or S?
S
200
a mapping of T maps a point from (-12, 7) to (18, 5)
What is function T? It only uses addition and subtraction.
T : (x, y) → ?
T : (x, y) →(x + 30, y - 2)
300
g(x) = 2x2 - 12
g(4) =
20
300
g(x) = x2 - 24
f(x) = 9x
g(f(x)) =
(in terms of X)
81x2 - 24
300
How tall is the tree?
32.9
300
T: (x, y) → (y, x-1)
S: (x, y) → (x+12, y-1)
S ◦ T : (12, -1) → ?
(11, 10)
300
How long is the hypotenuse of this triangle?
25.4 m
400
f(x) = x3 - 9x
f(4) =
28
400
f(x) = 2x2 - 32
g(x) = 7x
f(g(f(4))) =
-32
400
A ladder is leaning against a wall. The ladder is 1.8m long and the bottom of the ladder is 0.5m from the base of the wall. To be considered safe, a ladder must form an angle of between 70 and 90 degrees with the floor. Is this ladder safe?
yes, because the angle is 73.9 degrees
400
T: (x, y) → (2x + 2, y-3)
T3 (1, 3) → ?
(22, -6)
400
f(x) = 2x2
g(x) = 1.5x + 1
g(x) = 1.5x + 1
f(g(6)) =
200
500
g(x) = x2 - 5x + 2
g(g(6)) =
26
500
f(x) = -2x2 + 13
g(x) = 15x
g(f(f(g(2.5))))
-236
500
how much is angle B?
28.8
500
T: (x, y) → (x2, 1.5y)
S: (x, y) → (y, 2x)
T2 ◦ S ◦ T: (4, 2)
(81, 72)
500
Find both missing sides and the missing angle
x = ~3.5
other side = ~13.5
angle = 75