1.3 families of equations. what families of graphs have your studied? linear absolute value...
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1.3 Families of Equations
What families of graphs have your studied?
•Linear
•Absolute Value
•Quadratic •Square Root •Cubic•Cube Root
How do you recognize the various families?
Linear Family
Equation:
Graph:
y = mx + bAx + By + C = 0 Line: m = +
m = –m = 0
Examples:Graph the following linear equations:
y = 3x - 5
Domain--
Range--
Increasing/Decreasing?
Odd/Even
Examples:Graph the following linear equations:
2x – 3y = 12
Domain--
Range--
Increasing/Decreasing?
Odd or Even?
How do you recognize the various families?
Absolute Value Family
Equation:
Graph:
y = a|x – h| + k
(h,k)
(h,k)
a = – a = +
Examples:Graph the following absolute value equations:
y = |x|
Domain--
Range--
Increasing/Decreasing?
Odd or Even?
Examples:Graph the following absolute value equations:
y = |x - 2|+ 3
Domain--
Range--
Increasing/Decreasing?
Odd or Even
Examples:Graph the following absolute value equations:
y = |x + 6|+ 5
Domain--
Range--
Increasing/Decreasing?
Odd or Even
Examples:Graph the following absolute value equations:
y = -|x - 1|-3
Domain--
Range--
Increasing/Decreasing?
Odd or Even?
How do you recognize the various families?
Quadratic Family
Equation:
Graph:
Pattern:
y = a(x – h)2 + ky = ax2 + bx + c
a = –(h,k)
a = +
(h,k)
1, 3, 5
Examples:Graph the following quadratic equations:
y = x2
Domain--
Range--
Increasing/Decreasing?
Odd or Even
Examples:Graph the following quadratic equations:
y = (x-1)2
Domain--
Range--
Increasing/Decreasing?
Odd or Even?
Examples:Graph the following quadratic equations:
y = -(x-2)2 + 4
Domain--
Range--
Increasing/Decreasing
Odd or Even?
Examples:Graph the following quadratic equations:
y = x2 + 4x - 1
Hint: x = -b 2a
How do you recognize the various families?
Square Root Family
Equation:
Graph:
Pattern:
a = – a = +
y = a√x – h + k
(h,k)
or (h,k)
or
1, 3, 5
y = a(x – h)1/2 + k
Examples:Graph the following square root equations:
y = √x
Domain--
Range--
Increasing/Decreasing
Examples:
y = √x – 3 + 2
Graph the following square root equations:
Domain--
Range--
Increasing/Decreasing
How do you recognize the various families?
Cubic Family
Equation:
Graph:
Pattern:
y = a(x – h)3 + k
a = –(h,k)
a = +
(h,k)
1, 7
Examples:Graph the following cubic equations:
y = x3
Domain--
Range--
Increasing/Decreasing
Examples:Graph the following cubic equations:
y = x3 - 1
Domain--
Range--
Increasing/Decreasing?
Examples:Graph the following cubic equations:
y = -(x-2)3 + 4
Domain--
Range--
Increasing/Decreasing?
How do you recognize the various families?
Cube Root Family
Equation:
Graph:
Pattern:
a = – a = +
y = a 3√x – h + k
(h,k) (h,k)
1, 7
y = a(x – h)1/3 + k
Examples:
y = 3√x
Graph the following cube root equations:
Domain--
Range--
Increasing/Decreasing
Examples:
y = 3√x – 3 + 2
Graph the following cube root equations:
Domain--
Range--
Increasing/Decreasing?
Identify the family of graphs for the following equations:
Equation Family3x + 2y = 6
y = (x – 2)2 + 1
y = | x – 4 | + 6
y = 3x2 + 6x – 2
y = 2 x – 1 + 4
y = – 3 4 – x + 2
(x – 2)2 + (y – 6) 2 = 4
Identify the family of graphs for the following equations:
Equation Familyy = 2/3 | x – 4 | + 1
y = 1 – x
x = 5
x2 +y2 + 3x -1 = 0
x2 + y2 = 84
y = – 3 x + 1 – 3
y = – 2
Identify the family of graphs for the following equations:
Equation Familyy = – ( x – 4 ) 2
y = 2x2 + 1
y = 3/2 x – 2
y = –2 | x |
y = (x – 8)1/3 - 3
Average Rate of Change
f(x2) – f(x1) x2 - x1
Change in yChange in x
msec
A function y = f(x) is even iff(-x) = f(x)
A function y = f(x) is odd iff(-x) = -f(x)