Function Family Album
18
Function Family Album
-Q'elli Gonzales
Linear Function
Parent Function: f(x)=x
Equation of Inverse: f^-1(x)=y
Domain: (-∞,∞)
Range: (-∞,∞)
X-intercepts: (0,0)
Y-Intercepts: (0,0)
Linear
Vertical Shift
f(x)= x+3
V-Shift
Horizontal Shift
f(x)= x-3
H-Shift
Vertical Stretch
f(x)= 5x
V-Stretch
Reflection Over X-Axis
f(x)= -x
Reflect
Absolute Value Function
Parent Function: f(x)= |x|
Equation of Inverse: N/A
Domain: (-∞,∞)
Range: (0,∞)
X-Intercepts: (0,0)
Y-intercepts: (0,0)
Absolute
Value
Vertical Shift
f(x)= |x|-1
V-Shift
Horizontal Shift
f(x)= |x-1|
H-Shift
Vertical Stretch
f(x)= 2|x|
V-Stretch
Reflection Over X-Axis
f(x)= -|x|
Reflect
Quadratic Function
Parent Function: f(x)= x^2
Inverse Function: f^-1(x)= ñx
Domain: (-∞,∞)
Range: (0,∞)
X-Intercepts: (0,0)
Y-Intercepts: (0,0)
Quadratic
Vertical Shift
f(x)= (x^2)+3
V-Shift
Horizontal Shift
f(x)= (x-1)^2
H-Shift
Vertical Compression
f(x)= 1/2x^2
V-Shrink
Reflection Over X-Axis
f(x)= -x^2
Reflect
Square Root Function
Parent Function: f(x)= √x
Equation of Inverse: f^-1(x)= x^2
Domain: (0,∞)
Range: (0,∞)
X-Intercepts: (0,0)
Y-Intercepts: (0,0)
Square
Root
Reflecction Over X-Axis
f(x)= -√x
Reflect
Vertical Stretch
f(x)= 4√x
V-Stretch
Horizontal Shift
f(x)= (√x+3)
H-Shift
Vertical Shift
f(x)= (√x) +3
V-Shift
Cubic Function
Parent Function: f(x)= x^3
Equation of Inverse: f^-1(x)= 3^√x
Domain: (-∞,∞)
Range: (-∞,∞)
X-Intercepts: (0,0)
Y-Intercepts: (0,0)
Cubic
Vertical Shift
f(x)= (x^3)-4
V-Shift
Horizontal Shift
f(x)= (x-2)^3
H-Shift
Vertical Compression
f(x)= 1/4x^3
V-Shrink
Reflection Over X-Axis
f(x)= -x^3
Reflect
Cube Root Function
Parent Function: f(x)= 3^√x
Equation of Inverse: f^-1(x)= x^3
Domain: (-∞,∞)
Range: (-∞,∞)
X-Intercept: (0,0)
Y-Intercept:(0,0)
Cube
Root
Vertical Shift
f(x)= (3^√x)-5
V-Shift
Horizontal Shift
f(x)= (3^√x-6)
H-Shift
Vertical Stretch
f(x)= 4(3^√x)
V-Stretch
Reflection Over X-Axis
f(x)= -(3^√x)
Reflect
Rational Function
Parent Function: f(x)= 1/x
Equation of Inverse: f^-1(x)= 1/x
Domain: (-∞,0) U (0,-∞)
Range: (-∞,0) U (0,-∞)
X-Intercept: N/A
Y-Intercept: N/A
Rational
Vertical Shift
f(x)= (1/x)+6
V-Shift
Horizontal Shift
f(x)= (1/x+5)
H-Shift
Vertical Stretch
f(x)= 2(1/x)
V-Stretch
Reflection Over X-Axis
f(x)= -(1/x)
Reflect
Exponential Function
Parent Function: f(x)= 2^x
Equation of Inverse: f^-1(x)= ln(x)/ln(2)
Domain: (-∞,∞)
Range: (0,∞)
X-Intercept: N/A
Y-Intercept: (0,1)
Exponential
Vertical Shift
f(x)= (2^2)-7
V-Shift
Horizontal Shift
f(x)= (2^x-5)
H-Shift
Vertical Compression
f(x)= 1/4(2^x)
V-Shrink
Reflection Over X-Axis
f(x)= -(2^x)