Learning objectives
The student will perform parameter changes on a parent function. The student will observe the effects of the parameter changes on the transformed graph.Real world application
Transforming a parent function can produce mathematical models that are useful in many different applications. Transformations provide a way to create relations that model relationships as diverse as population growth, projectile motion, constant rate of change, and inverse variation.Start
Reset
Reset
Choose a type of transformation from the tabs below. Then select a parent function from the drop-down menu.
Use the arrows to change the parameter(s) in the equation. Changing a parameter will have a predictable effect on the graph of the function.
Function:
| af(x) = ax = |
1
10
1
10
|
x |
| af(x) = ax2 = |
1
10
1
10
|
x2 |
| af(x) = a√ x = |
1
10
1
10
|
√ x |
| af(x) = a |
1
x
|
= |
1
10
1
10
|
1
x
|
| af(x) = ax3 = |
1
10
1
10
|
x3 |
| af(x) = a | = |
1
10
1
10
|
| af(x) = a2x = |
1
10
1
10
|
2x |
| af(x) = a10x = |
1
10
1
10
|
10x |
| af(x) = aex = |
1
10
1
10
|
ex |
| af(x) = a|x| = |
1
10
1
10
|
|x| |
| af(x) = alog2x = |
1
10
1
10
|
log2x |
| af(x) = alogx = |
1
10
1
10
|
logx |
| af(x) = alnx = |
1
10
1
10
|
lnx |
| f(x) = x | |||
|
| f(x) = √ x | |||
|
|
|||
|
| f(x) = |x| | ||||
|
| f(x) = logx | ||||
|
| f(x) = lnx | ||||
|
Function:
| f(bx) = bx = |
1
10
1
10
|
x |
| f(bx) = (bx)2 = ( |
1
10
1
10
|
x)2 |
| f(bx) = √ bx = |
1
10
1
10
|
x |
|
f(bx) =
|
1
bx
|
= |
1
|
| f(bx) = (bx)3 = ( |
1
10
1
10
|
x)3 |
| f(bx) = | = |
1
10
1
10
|
x |
| f(bx) = 2bx = 2 |
1
10
1
10
|
x |
| f(bx) = 10bx = 10 |
1
10
1
10
|
x |
| f(bx) = ebx = e |
1
10
1
10
|
x |
| f(bx) = |bx| = | |
1
10
1
10
|
x| |
| f(bx) = log2 (bx) = log2( |
1
10
1
10
|
x) |
| f(bx) = log(bx) = log( |
1
10
1
10
|
x) |
| f(bx) = ln(bx) = ln( |
1
10
1
10
|
x) |
| f(x) = x | |||
|
| f(x) = x2 | ||||||
|
| f(x) = √ x | |||
|
|
|||||||
|
| f(x) = x3 | ||||||
|
|
|||
|
| f(x) = 2 x | |||||
|
| f(x) = 10 x | |||||
|
| f(x) = e x | |||||
|
| f(x) = | x | | ||||
|
| f(x) = log2 x | ||||||
|
| f(x) = log x | ||||||
|
| f(x) = ln x | ||||||
|
Function:
| f(x – | c | ) = x – c | = |
| x – |
0
10
|
| f(x – c) = (x – c)2 | = |
| (x – |
0
10
|
)2 |
| f(x – c) = √ x – c | = |
| x – |
0
10
|
| f(x – c) = |
1
x – c
|
= |
|
1
|
| f(x – c) = (x – c)3 | = |
| (x – |
0
10
|
)3 |
| f(x – c) = | = |
| x – |
0
10
|
| f(x – c) = 2x – c | = |
| 2 | x – |
0
10
|
| f(x – c) = 10x – c | = |
| 10 | x – |
0
10
|
| f(x – c) = ex – c | = |
| e | x – |
0
10
|
| f(x – c) = |x – c| | = |
| |x – |
0
10
|
| |
| f(x – c) = log2(x – c) | = |
| log2(x – |
0
10
|
) |
| f(x – c) = log(x – c) | = |
| log(x – |
0
10
|
) |
| f(x – c) = ln(x – c) | = |
| ln(x – |
0
10
|
) |
| f(x) = x | |||
|
| f(x) = x2 | ||||||
|
f(x – c) = x2
|
| f(x) = √ x | ||
|
|
|||||
|
| f(x) = x3 | ||||||
|
f(x) = x3
|
|
|||
|
| f(x) = 2x | ||
|
| f(x) = 10x | ||
|
| f(x) = ex | ||
|
| f(x) = |x| | |||
|
| f(x) = log2 x | |||
|
| f(x) = log x | |||
|
| f(x) = ln x | |||
|
Function:
| f(x) + d = x + d | = |
| x + |
0
10
|
| f(x) + d = x2 + d | = |
| x2 + |
0
10
|
| f(x) + d = √ x + d | = |
| √ x | + |
0
10
|
| f(x) + d = |
1
x
| + d | = |
|
1
x
|
+ |
0
10
|
| f(x) + d = x3 + d | = |
| x3 + |
0
10
|
| f(x) + d = | + d | = |
| + |
0
10
|
| f(x) + d = 2x + d | = |
| 2x + |
0
10
|
| f(x) + d = 10x + d | = |
| 10x + |
0
10
|
| f(x) + d = ex + d | = |
| ex + |
0
10
|
| f(x) + d = |x| + d | = |
| |x| + |
0
10
|
| f(x) + d = log2(x) + d | = |
| log2(x) + |
0
10
|
| f(x) + d = log(x) + d | = |
| log(x) + |
0
10
|
| f(x) + d = ln(x) + d | = |
| ln(x) + |
0
10
|
| f(x) = x | |||
|
| f(x) = x2 | |||
|
| f(x) = √ x | ||
|
|
||||
|
| f(x) = x3 | |||
|
|
|||
|
| f(x) = 2x | |||
|
| f(x) = 10x | |||
|
| f(x) = ex | |||
|
| f(x) = |x| | ||||
|
| f(x) = log2(x) | |||
|
| f(x) = log(x) | |||
|
| f(x) = ln(x) | |||
|
Function:
| a | f | b | (x – | c | ) | + | d = |
| a | b | (x – | c | ) | + | d = |
|
1
10
1
10
|
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | b | (x – | c | ) | 2 | + | d = |
|
1
10
1
10
|
1
10
1
10
|
(x – |
0
10
|
) | 2 | + |
0
10
|
| a | f | b | ( x – | c | ) | + | d = |
| a | b | ( x – | c | ) | + | d = |
|
1
10
1
10
|
1
10
1
10
|
( x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a |
1
|
+ | d = |
|
1
10
1
10
|
1
|
+ |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | b | (x – | c | ) | 3 | + | d = |
|
1
10
1
10
|
1
10
1
10
|
(x – |
0
10
|
) | 3 | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | b | ( x – | c | ) | + d = |
|
1
10
1
10
|
1
10
1
10
|
( x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | 2 | b | (x – | c | ) | + | d = |
|
1
10
1
10
|
2 |
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | 10 | b | (x – c) | + | d = |
|
1
10
1
10
|
10 |
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | e | b | (x – c) | + | d = |
|
1
10
1
10
|
e |
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | b | (x – | c | ) | + | d = |
|
1
10
1
10
|
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | log2 | b | (x – | c | ) | + | d = |
|
1
10
1
10
|
log2 |
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | log | b | (x – | c | ) | + | d = |
|
1
10
1
10
|
log |
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| a | f | b | (x – | c | ) | + | d = |
| a | ln | b | (x – | c | ) | + | d = |
|
1
10
1
10
|
ln |
1
10
1
10
|
(x – |
0
10
|
) | + |
0
10
|
| f(x) = x | ||||||||||||
|
| f(x) = x 2 | |||||||||||||||
|
| f(x) = √ x | ||||||||||||||||
|
|
|||||||||||||
|
| f(x) = x 3 | |||||||||||||||
|
|
||||||||||||||||
|
| f(x) = 2 x | |||||||||||||||
|
| f(x) = 10 x | |||||||||||||||
|
| f(x) = e x | |||||||||||||||
|
| f(x) = | x | | ||||||||||||||||
|
| f(x) = log2 x | |||||||||||||||
|
| f(x) = log x | |||||||||||||||
|
| f(x) = lnx | |||||||||||||||
|