parent functions constant function inverse linear (identity)inverse squared absolute value...
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PARENT FUNCTIONSConstant Function InverseLinear (Identity) Inverse SquaredAbsolute Value ExponentialQuadratic LogarithmicCubic SineSquare Root CosineSignum Greatest Integer
Constant Function Inverse or Rational
Linear (Identity) Inverse Squared
Absolute Value Exponential
Quadratic Logarithmic
Cubic Sine
Square Root Cosine
Signum Greatest Integer
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or2) Click on a Specific Function Below for the Properties.
3) Use the button to return to this menu.
Constant Function
f(x) = awhere a = any
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Constant Function
Domain: ,
Range: 2y
Parent Equation: f(x) = 2
Constant Function
Parent Equation: f(x) = 2
x – intercept:
y – intercept: 0, 2
None
Constant Function
Graph Description: Horizontal Line
Table:x y
-2 2
-1 2
0 2
1 2
2 2Parent Equation: f(x) = 2
Linear Function(Identity)
f(x) = x
Linear Function(Identity)
Domain: ,
Range: ,
Parent Equation: f(x) = x
Linear Function(Identity)
Parent Equation: f(x) = x
x – intercept:
y – intercept: 0, 0
0, 0
Linear Function(Identity)
Parent Equation: f(x) = x
Table:x y
-2 -2
-1 -1
0 0
1 1
2 2
Graph Description: Diagonal Line
Absolute Value Function
f(x) = │x │
Absolute Value Function
Domain: ,
Range: 0,
Parent Equation: f(x) = │x │
Absolute Value Function
Parent Equation: f(x) = │x │
x – intercept:
y – intercept: 0, 0
0, 0
Absolute Value Function
Table:x y
-2 2
-1 1
0 0
1 1
2 2Parent Equation:
Graph Description: “V” - shaped
f(x) = │x │
f(x) = x 2
Quadratic Function
f(x) = x 2
Quadratic Function
Domain: ,
Range: 0,
Parent Equation:
Quadratic Function
Parent Equation:
x – intercept:
y – intercept: 0, 0
0, 0
f(x) = x 2
f(x) = x 2
Quadratic Function
Table:x y
-2 4
-1 1
0 0
1 1
2 4Parent Equation:
Graph Description: “U” - shaped
Cubic Function
f(x) = x 3
Cubic Function
f(x) = x 3
Domain: ,
Range: ,
Parent Equation:
Cubic Function
f(x) = x 3
Parent Equation:
x – intercept:
y – intercept: 0, 0
0, 0
Cubic Function
f(x) = x 3
Parent Equation:
Table:x y
-2 -8
-1 -1
0 0
1 1
2 8
Graph Description: Squiggle, Swivel
f(x) = x
Square Root Function
f(x) = x
Square Root Function
Domain: 0,
Range: 0,
Parent Equation:
f(x) = x
Square Root Function
Parent Equation:
x – intercept:
y – intercept: 0, 0
0, 0
f(x) = x
Square Root Function
Parent Equation:
Table:x y
0 0
1 1
4 2
9 3
16 4
Graph Description: Horizontal ½ of a Parabola
f(x) = 1x
Inverse Function or Rational Function(Reciprocal of x)
f(x) = 1x
Inverse Function or Rational Function(Reciprocal of x)
Parent Equation:
Domain:
, 0 0,or
Range:
, 0 0,or
f(x) = 1x
Inverse Function or Rational Function(Reciprocal of x)
Parent Equation:
x – intercept:
y – intercept: None
None
Inverse Function or Rational Function(Reciprocal of x)
Table:x y
-2 -0.5
-1 -1
0 Error
1 1
2 0.5f(x) = 1x
Parent Equation:
Graph Description: Opposite “L” Curves in 1st and 3rd
Quadrants
Inverse Squared Function
(Reciprocal of x 2)
f(x) = 1x 2
Inverse Squared Function
(Reciprocal of x 2)
f(x) = 1x 2Parent Equation:
Domain:
, 0 0,or
Range:
0,
Inverse Squared Function
(Reciprocal of x 2)
f(x) = 1x 2
x – intercept:
y – intercept: None
None
Parent Equation:
Inverse Squared Function
(Reciprocal of x 2)
f(x) = 1x 2Parent Equation:
Table:x y
-2 0.25
-1 1
0 Error
1 1
2 0.25
Graph Description: Symmetrical “L” Curves in 1st and 2nd
Quadrants
Exponential Function
( ) xf x b
b = base and
x = exponent
f(x) = 2x
Exponential Function
Domain: ,
Range: 0,
Parent Equation:
f(x) = 2x
Exponential Function
x – intercept:
y – intercept: 0, 1
None
Parent Equation:
f(x) = 2x
Exponential Function
Table:x y
-2 0.25
-1 0.5
0 1
1 2
2 4Parent Equation:
Graph Description: Backwards “L” Curves
f(x) = log x
Logarithmic Function
f(x) = log x
Logarithmic Function
0,
Range: ,
Parent Equation:
Domain:
f(x) = log x
Logarithmic Function
x – intercept:
y – intercept: None
1, 0
Parent Equation:
Logarithmic Function
Table:x y
-2 Error
-1 Error
0 Error
1 0
2 0.301
Parent Equation: Graph Description: Upside Down “L” curve in
1st and 4th Quadrant
f(x) = log x
Step Function(Greatest Integer)
f(x) = [x]
Step Function(Greatest Integer)
f(x) = [x]
Domain: ,
Range: y y Z
Parent Equation:
Step Function(Greatest Integer)
f(x) = [x] Parent Equation:
x – intercept:
y – intercept: 0, 0
0, 1
Step Function(Greatest Integer)
f(x) = [x] Parent Equation:
Graph Description: Stair Steps
Table:x y-2 -2
-1 -1
0 0
1 1
2 2
Signum Function
Signum Function
Domain: ,
Range: 1, 0, 1y
Parent Equation:
Signum Function
Parent Equation:
x – intercept:
y – intercept: 0, 0
0, 0
Signum Function
Table:x y-2 -1
-1 -1
0 0
1 1
2 1
Parent Equation:
Graph Description: Left and Right Arrows
Opposite Directions
Sine Functionf(x) = sin x
Sine Function
f(x) = sin x
Domain: ,
Range: 1, 1
Parent Equation:
Sine Function
f(x) = sin x
x – intercept:
y – intercept: 0, 0
,x x n n Z
Parent Equation:
Sine Function
f(x) = sin x
Table:x y-2 -0.9093
-1 -0.8415
0 0
1 0.8415
2 0.9093
Parent Equation: Graph Description: Wavy, above and below x-axis
with y-int at (0, 0)
Cosine Functionf(x) = cos x
Cosine Function
f(x) = cos x
Domain: ,
Range: 1, 1
Parent Equation:
Cosine Functionf(x) = cos x
x – intercept:
y – intercept: 0, 1
,2
x x n n Z
Cosine Function
f(x) = cos x
Table:
x y-2 -0.4161
-1 0.5403
0 1
1 0.5403
2 -0.4161
Parent Equation: Graph Description: Wavy, above and below x-axis
with y-int at (0, 1)