Foundations
Simplify: 3x + 4x - 2
7x - 2
Solve: x + 6 = 12
x = 6
Find the slope of a line passing through (2, 3) and (4, 7).
m = 2
Solve by substitution: y = 2x + 1 and y = x + 4
x = 3, y = 7
efine the domain of a function.
: The set of input values
What is the correct order of operations?
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
Solve: 3x - 4 = 11
x = 5
Write the slope-intercept form: slope = 3, y-intercept = -2
y = 3x - 2
Solve by elimination: 2x + y = 10, x - y = 2
x = 4, y = 2
Define the range of a function.
The set of output values
Identify the property: (2 + 3) + 4 = 2 + (3 + 4)
Associative Property of Addition
Solve: 2(x + 3) = 10
x = 2
Find the x-intercept of y = 2x - 6
(3, 0)
What does it mean if two lines have the same slope but different intercepts?
They are parallel and never intersect
Domain and range of f(x)=2x+3f(x) = 2x + 3f(x)=2x+3
Domain = all real numbers; Range = all real numbers (linear function, no restrictions).
Translate into an expression: "five more than twice a number n."
2n + 5
Solve x-2=5
x=7
Write the equation of a line in standard form with slope 2 and y-intercept 4
2x - y = -4
Solve the system: y = x + 1 and y = -x + 5
x = 2, y = 3
Given points (−2,3),(0,5),(2,7)(-2,3), (0,5), (2,7)(−2,3),(0,5),(2,7) — domain and range
Domain = {−2, 0, 2}\{-2,\,0,\,2\}{−2,0,2}. Range = {3, 5, 7}.\{3,\,5,\,7\}.{3,5,7}.
Simplify using the distributive property: 4(3x - 2)
12x - 8
2x + 1 < 7
x < 3
A line has a slope of 1/2 and passes through (2, 4). Write its equation.
equation.y - 4 = (1/2)(x - 2) or y = (1/2)x + 3
A company sells two types of tickets: regular and VIP. Regular tickets cost $25, VIP tickets cost $40. The company made $2,800 selling 100 tickets total. Write and solve a system of equations to find how many of each ticket type were sold.
25r+40v=2800
or f(x)=x−2f(x) = \sqrt{x - 2}f(x)=x−2 — domain and range
Domain: [2,∞) Range: [0,∞).