Function Families
Function Properties
Polynomial Addition and Subtraction
Factoring and Solving Polynomials
Properties of Quadratics
100
Write the parent function and sketch a graph for a LINEAR function.
y = mx + b OR f(x) = x
100
Describe the transformations made to this parent function: g(x) = -|x| + 3
reflection, moved up (vertical translation)
100
(4x^2 - 3) + (5x^2 + 6)
9x^2 + 3
100
Factor:
3x^3 - 6x^2
3x^2(x - 2)
100
Identify the axis of symmetry:
x = 3
200
Write the parent function and sketch a graph for a QUADRATIC function.
f(x) = x2
200
Describe the transformations made to this parent function:
g(x) = 1/2|x - 4|
vertical shrink, moved right (horizontal translation)
200
(8x^2 + 2x + 9) - (3x^2 + 6x + 4)
5x^2 - 4x + 5
200
Factor:
x^2 + 7x + 12
(x + 4)(x + 3)
200
Indentify the zeros:
-4 and 0
300
Write the parent function and sketch a graph for an ABSOLUTE VALUE function.
f(x) = |x|
300
State the domain and range:
D: all reals
R: y ≤ 2
300
(-2x^2 - 10) + (4x^2 +11x)
2x^2 + 11x - 10
300
Factor:
x^2 - 9x + 18
(x - 6)(x - 3)
300
Find the axis of symmetry:
f(x) = x^2 + 6x - 16
x = -3
400
Write the parent function and sketch a graph for an EXPONENTIAL function.
f(x) = bx OR f(x) = 2x
400
State the domain and range:
D: all reals
R: y > 3
400
(-7x^3 + 2x - 1) - (3x^2 + 6x + 4)
-7x^3 - 3x^2 - 4x - 5
400
Solve:
3x^2 - 3x - 18 = 0
3 and -2
400
Find the vertex:
f(x) = x^2 + 6x - 16
(-3, -25)
500
Which function family does f(x) = 3 belong to?
linear
500
Evaluate: f(3)
2
500
(5x^2 - 2x + 9) - (-7x^2 + 6x - 4)
12x^2 - 8x+13
500
Solve:
2x^2 + 5x = -3
-3/2 and -1
500
Find the zeros:
f(x) = x^2 + 6x - 16
-8 and 2