composition of functions
inverse of functions
Rate of change
Key features of functions
transformation of functions
100
f(x) = 3x + 4
g(x) = x - 2
Find f(g(2))
f(g(2)) = 4
100
Find the inverse of the function
f(x) = -4x + 1
f-1(x) = x - 1 / -4
or
f-(x) = -1/4 x + 1/4
100
Find the average rate of change:
f(x) = 4x2 Find the interval [-2,3]
4
100
Identify the end behavior(correct form)
As x is approaching - infinity, y is approaching +infinity
As x is approaching +infinity, y is approaching + infinity
100
Describe the transformation:
f(x) = x3
g(x) = 3 (x + 1)3
-shift one unit to the left
-Vertical translation of a factor of 3
200
f(x) = x + 3
g(x) = x2 - 4x
Find g(f(3))
g(f(3)) = 20
200
Find the inverse of
f(x) = x + 3
f-1(x) = x - 3
200
Find the average rate of change of
f(x) = - x 2
over the interval [5,10]
-15
200
Identify the end behavior(correct format)
As x is approaching - infinity, y is approaching -infinity
As x is approaching +infinity, y is approaching + infinity
200
Describe the transformation:
g(x) = x2
f(x) = (x - 3)2 + 4
-Shifts 3 units right
-Shifts 4 units up
300
h(x) = 4x - 12
f(x) = 6x2 +2
Find f(h(4))
f(h(x)) = 98
300
Find the inverse function of
f(x) = (7x + 18) / 2
f-1(x) = (2x - 18) / 7
300
Find the average rate of change
g(x) = 5x + 16
over the interval [ -13, -7]
5
300
Identify the end behavior( correct format)
As x is approaching - infinity, y is approaching +infinity
As x is approaching +infinity, y is approaching - infinity
300
Write the new equation for the transformation:
f(x) = x2
-translates up 1 unit
-translates left 3 units
- expands vertically by a factor of 3
g(x) = 3(x+3)2 +1
400
f(x) = x + 4
g(x) = x2 - 6x
Find f(g(x))
f(g(x)) = x2 -6x +4
400
find the inverse of
g(x) = - x + 3
g-1(x) = -x + 3
400
Find the average rate of change of
h(x) = -12 + 1
over the interval [- 8, -7]
-12
400
How many turning points does this graph have?
How many intercepts does this graph have?
4
4
400
Write a transformed equation for the following
f(x) = x3
-expanded vertically by a factor of 4
-reflect across the x-axis
-translate left 2 units
-translate up 3 units
g(x) = -4(x + 2)3 + 3
500
f(x) = 6x - 2
g(x) = x2 + 5x - 4
Find g(f(x))
g(f(x)) = 36x2 - 19x
500
Find the inverse of
h(x) = 3 x3 - 3
h-1(x) = cube root of ((x + 3)/ 3)
500
Find the average rate of change
k(x) = -17x + 15
over the interval [-4,3]
-17
500
How many turning points does this graph have?
How many intercepts does this graph have?
1
2
500
Write a transformed equation for the following
f(x) = x
-compress vertically by a factor of 1/3
-reflect across the x-axis
-translate right 2 units
-translate down 3 units
g(x) = -1/3(x - 2) -3