Functions
Given the relation (0, 3) (2, 6) (4, 9), do they represent a function? Explain why or why not.
Yes, because every input has exactly one output
What is the average rate of change between the following two coordinate points? (9,0) and (3, 5)
f(x) = x g(x) = 3x + 2
Find f(g(5))
f(g(5))= 17
Write an ABSOLUTE VALUE equation that shows it shifting 5 units up
y=|x|+5
If the coordinate point (- 6, 7 ) is on an EVEN function what other coordinate point must be on the graph?
(6, 7)
f(x) = -3x + 8
Find f(9)
f(9) = -19
Find the average rate of change from when x = 1 to x=7
x = 0 1 2 3 4 5 6 7
y= -7 -3 1 5 9 13 17 21
average rate of change = 4
f(x) = 5x + 2 g(x) = 7x - 5
Find g(f( - 1))
g(f ( -1) ) = - 26
What transformation is happening to the absolute value equation?
y=|x+2|-4
Left 2 Down 4
Are the following equations inverses of each other?
f(x) =3x - 2
f-1(x) = 3x + 2
If g(x) = 37, what is x?
x = 5
f(x) = 3x2 + 1
Find the average rate of change from when x = -4 to when x = 7
Average rate of change = 9
f(x) = 2x2 + 3 g(x) = -3x2
Find f(g( -2 ))
f(g( -2 ))= 291
When an equation as a negative number at the beginning, what kind of change is happening?
(be as specific as you can)
It is reflecting over the x axis
Find the inverse of the f(x)
f(x) = -7x + 6
SHOW WORK
f-1(x) = x - 6 / -7
f(x) = 3x2 - 5x +29
Find f(-5)
f(-5) = 129
f(x) = - 4x2 - 6x + 1
Find the average rate of change from when x = -3 to when x = 3
Average rate of change = - 6
f(x) = 8x + 1 g(x) = 4x +5
Find f(g(x))
f(g(x)) = 32x + 41
What kind of shift is happening?
f(x) = -3|x| + 8
Reflecting over the x axis
stretching by 3
Going up 8
Find the Inverse Function of f(x)
f(x) = x2 + 6
f-1(x)=sqrt(x-6)
f(x) = x2 -6 g(x) = - 2x - 7
Find f(g(x))
f(g(x)) = 4x2 + 28x + 43
Write a Quadratic Equation that shows the following transformation:
Reflecting over axis
Stretch by 2
Left 6 and Up 1
y = -2(x+6)2 + 1
Does the function y = x3 + 3x represent an odd, even, or neither function?
SHOW WORK
ODD