Families by Graph Features
Function Equations (name the family)
Function Transformations
Domain and Range
Evaluate the function
100
This function family's graph is a line.
Linear Functions
100
f(x)= -2x + 4
LINEAR
100
Parent function: y = x
Graph moved up 3 and got twice as steep
What is the new equation?>
y = 2x + 3
100
What is the domain of of the parent function y= x
All real numbers
100
f(x) = 2x - 6
Evaluate for x = 4
f(4) = 2
200
This function family's graphs make a smooth curve. They have a minimum or a maximum. It looks like a U.
QUADRATIC
200
f(x)=|8x-2|-3
ABSOLUTE VALUE
200
Parent function: y = x2
Graph moved down 2
What is the new equation?
y = x2 -2
200
The range is what values of a function?
The y values
200
g(x)= 3x
Evaluate for x = -5
g(-5) = -15
300
The graph looks like a V. They have a minimum or a maximum.
ABSOLUTE VALUE
300
A(t)=2,000(1.02)t
EXPONENTIAL
300
Parent function: y = x2
The graph moved left 3, got twice as wide, and moved down 5... What is the new equation?
y= (x+3)2 - 5
300
When a function has a maximum or minimum what is affected: domain or range?
Range
300
f(x)= x2
Evaluate f(3)
f(3) = 9
400
This function family's graph has a smooth curve. They either increase or decrease. The variable x is the exponent.
EXPONENTIAL
400
g(x)= (x+2)(x-3)
QUADRATIC (in factored form)
400
Transformed function is y = 2(x-3)
The parent function was 2x
How did the graph change from the original function? Describe the transformation
It moved right 3
400
What is the range of the quadratic function?
y > -4
400
f(x) = 5x
Evaluate for f(-2)
-10
500
What is another name for the graph of a quadratic function?
Parabola
500
f(x) = x2 +3x - 4
Quadratic Function (in standard form)
500
The new function is
f(x)= -x +3
How did it change from the original function, y= x?
Reflection and up 3
500
What is the domain of the exponential function?
All real numbers
500
f(x) = 2x
Evaluate for x = 2
f(2) = 4