Vocabulary
True or False
Exponentials
What is ___?
Transforming exponential functions
100
an expert in or a student of mathematics.
What is a Mathematician?
100
23 = 2 x 3 = 6
False
23 = 2 x 2 x 2 = 8
100
What are the a & b values of this exponential function?
f(x) = 1 . 3x
a = 1 (the y-intercept)
b = 3 (the common ratio)
100
What is the y-intercept of this table?
6
On a table, you find the y-intercept across from the 0 in the x column
100
Translate the function f(x) = 1 . 3x to move 3 spaces to the right
f(x) = 1 . 3(x-3)
200
The ratio between any two consecutive terms in a geometric sequence
2,4,8,16,... = 2
What is a Common Ratio?
200
In f(x) = 3 . 2x
3 is the y-intercept
TRUE
f(x) = a . b
a= y-intercept
b= common ratio
200
What is the horizontal asymptote of this graph?
The horizontal asymptote is 3
y = 3
200
a = y-intercept
b = common ratio
200
What is the function f(x)? Translate the function 3 spaces to the right and up 2. What is the new function g(x)?
f(x) = 1 . 3x
g(x) = 1 . 3(x-3) + 2
300
The number of times the base is used as a factor
23
What is the Exponent?
300
This graph is Increasing
TRUE
We read graphs from the left to the right
300
Evaluate the function.
f(x) = 1/3 . 6x at x = 2
f(2) = 1/3 . 62
f(2) = 1/3 . 36
f(2) = 36/3
f(2) = 12
300
f(x) = 2 . 4(x-3) + 5
Identify the values of a, b, h, & k
f(x) = a . b(x-h) +k f(x) = 2 . 4(x-3) + 5
a=2
b=4
h=3
k=5
300
Translate y = 10x to move 2 units to the right. Also translate the function to move 2 units down.
y=10x-2 will translate it 2 units to the right
y=10x -2 will translate it 2 units down
400
f(x) = a . bx
What is an Exponential Function?
400
The h-value produces a horizontal translation (left/right) while the k-value produces a vertical translation (up/down)
TRUE
f(x) = a . b (x-h) + k
400
Make a table of values for function:
f(x) = 4 . 1/2x
X Y-1
0
1
2
f(x) = 4 . 1/2x
X Y
-1 8
0 4
1 2
2 1
400
What is an equation that represents the function?
f(x) = 20 . (1/2)x
400
Translate the function f(x) = 2x to reflect over the y-axis and over the x-axis.
y = 2-x reflects over the y=axis
y = -2x reflects over the x-axis
500
A horizontal line that a function gets closer and closer to, but never intersects.
What is a Horizontal Asymptote?
500
This table matches this function. f(x) = 3(1/2)x
X Y
-1 6
0 3
1 1.5
2 0.75
TRUE
500
What are the y values of this function?
f(x) = 3 . (1/2)x
X Y
-2
-1
0
1
2
X Y
-2 12
-1 6
0 3
1 1.5
2 0.75
500
What is the function that would translate f(x) four space UP
f(x) = 1 . 2x
f(x) = 1 . 2x + 4
500
Make a table for g(x) = 3 . 2x +1
X Y
-1
0
1
2
Then translate g(x) = 3 . 2x
to move to the left 2 and down 2
X Y
-1 5/2
0 4
1 7
2 13
g(x) = 3 . 2(x+2) -2