Properties of Real Numbers
a + b = b + a
a x b = b x a
What is Commutative?
-(3x-4y-7)
=-3x + 4y - 7
For f(x)= 4x2 - 3 =, Find:
f (0)
(0,-3)
The point in which the graph crosses the x-axis
What is the x-intercept?
What is the slope (m)?
a (b + c) = ab + ac
a (b - c) = ab - ac
(a + b) c = ac + bc
What is Distributive?
2 (-4x-8)
=2 (-4x + 8)
=-8x+16
For R(x) = 100x- x3, find:
R (10)
(10,0) Also known as the X-Intercept
(0,-3)
What is y-intercept?
Given two points (x1,y1) and (x2,y2) find the slope.
(y2-y1)/(x2-x1)
Rational Numbers: (2/3), 7, -0.4
Irrational Numbers: √ 2, π (Pie), 1.345992703759
What are Real Numbers?
-4y-(3x-7y)
=-4y-3x+7y
=-3x-3y
Used to TEST if a graph represented by y is a function of x.
What is the Vertical Line Test?
The point where the graph crosses the y-axis.
What is the y-intercept?
Special Slopes: m = 0
What are Horizontal Lines?
Division by 0
What is Undefined?
-7(-3p-15q+14)
=21p + 105q - 98
For f(x)=3x+2 and g(x)= 5- x2, find:
(g-f)(x)
-x2 - 3x +3
(2,0)
What is x-intercept?
Special Slopes: m = undefined
What are Vertical Lines?
a x (1/a) = 1
(1/a) x a = 1
What is Multiplicative Inverse?
(1/2)(2x+4)-(1/3)(9x-6)
=(x+2)-3x+2
=-2x+4
Find the Domain and Range of:
x -3 0 1 -5 0 2 5 15 1
y -3 -4 9 8 0 -2 5 12 -5
D = {-5, -3, 0, 1, 2, 5, 15}
R = {-5, -4, -3, -2, 0, 5, 8, 9, 12}
To find the y-intercept in the following equation of the line in Standard form:
3x-2y = 6
What is let x = 0?
Find the slope of the line that passes through the points (3,7) and (3,-10).
m = 7 - (-10)/3-3 = 17/0
The slope is undefined. The line is vertical.