Function Family Album Project Bryan Ren Per 7
3
Transformation:
Aboslute Value:
h = shift left or right
k = shift up or down
Transformation:
Domain: All real number
Range: y >-1
X intercept: x = 0.369
Y intercept: y = -0.333
Asymptote: y=-1
Equation:
2(3)^(x -1) -1
Inverse:
log3((x+1)/2) + 1
Vertical stretch of 2
Shift right 1
Shift down
Parent function:
|x|
Standard form:
|x - h|+ k
Transformation:
a|x - h| + k
a = vertical stretch or shrink
Shift left 2
Shift up 2
Domain:
All real numbers
Range: (negative infinity, 2)
x intercept: x = -2.667 or -1.333
y intercept: y=-4
Equation:
-3|x + 2| + 2
Inverse:
-(x + 5)/3 or
(x - 1)/3
Flip over the x axis and vertical stretch of 3
Logarithmic:
h = shift left or right
k = shift up or down
Parent:
log(x)
Standard form:
log(b)^x
Transformation:
alogb(x + h) + k
a = vertical stretch or shrink
Transformation:
Square Root:
a = vertical shirnk or stretch
h = shift right or left
k = shift up or down
Parent function: x^1/2
Standard form:
(x-a)^1/2 + b
Transformation:
a(x-h)^1/2 + k
Exponential:
Equation:
1/2 (x - 1)^1/2 -1
Inverse:
4(x + 1)^2 + 1
Vertical shrink of 1/2
Shift right 1
Shift down 1
domain: (1, infinity)
range: (-1. infinity)
x intercept:
x = 5
y intercept:
no y intercept
h = shift left or right
k = shift up or down
Parent:
b^x
Standard form
a(b)^x
Transformation:
a(b)^(x + h) +k
a = vertical shrink or stretch
Transformation:
Equation:
y = 2(x - 1)^2 - 3
Inverse:
y = (x -3/2) ^ 1/2+ 1
Vertical Stretch of 2
Shift right 1
Shift down 3
domain:
All real numbers
range:
(-3, infinity)
x intercept: x = -0.225 or 2.225
y intercept: y = -1
Piecewise:
Transformation:
Quadratic:
Linear
1.
Equation:
Linear: Slope 1/2 y intercept 3
Absolute value: Vertical stgretch of 2, shift right 6, and shfit down 13
h = shift left or right
k = shift or down
x intercept:
x = 1.192
y intercept:
doesn't hit y axis
asymptote:
x = 1
h = shift left or right
k = shift up or down
Equation:
2log3(x-1) + 3
Inverse:
3 (2x-3)/2 + 1
Vertical stretch of 2
Shift right 1
Shift up 3
Domain:
x>1
Range: All real numbers
Parent function: y=x
Standard form: y=mx+b
How to transform:
y = a(x - h) + k
a = stretch or compress
vertically
Parent function: x^2
Standard form: ax^2 + bx + c = 0
transformation:
y = a(x - h)^2 + k
a = vertical shrink or stretch
Quadratic: Vertical shrink of 1/2 and shift down 2
Transformation
Domain:
All real numbers
Range:
All real numbers
y intercept: y = 7
x intercept: x = -1.167
Starting Equation:
y = 2x + 3
Equation:
y= 3(2x + 2) -1
Inverse:
y = 1/6x - 5/6
Vertical Stretch of 3
Shift left 2
Shift down 1
Nature
Function Family Album Project
Bryan Ren
Per 7