Linear Equations
Solve for x: 3x+ 7 = 22
x=5
If f(x) = 2x+1, find f(-3)
f(-3) = 2(-3)+1 = -5
What is the simplified form of the expression x4 * x3
x7
What type of circle is used on a number line when graphing the inequality x > 5?
An open circle
Solve and check: 4(x - 2) = 2x + 6
4x-8=2x+6 --> 2x=14 --> x=7
Identify the slope and y-intercept of y = −1/2 x + 4.
slope = -1/2
y-intercept = 4
What is the degree of the polynomial 4x3 - 5x2 +2x - 1?
3 or cubic
The algebraic method that is best to use first when one of the equations in a system is already solved for a single variable, such as y = 2x - 3.
Substitution
A line passes through (2,5) and has slope 2. Write an equation in slope-intercept form.
y=3x-1
State whether the relation given by y = x2 − 4x + 3 is a function and explain briefly.
Yes, it assigns exactly one y to each x (it's a function)
What is the leading coefficient of the polynomial 7x² - 8x⁵ + 3x?
-8
Yes or No: Is the origin (0,0) a valid solution to the following system?
y < x+4
y > 2x-1
Yes, because 0 < 4 and 0 > -1 are both true.
Solve (2x-1)/3 - (x+2)/4 = 1
Multiply by 12: 4(2x−1) − 3(x+2) = 12 → 8x−4 −3x−6 =12 → 5x −10 =12 → 5x =22 → x = 22/5
Given f(x) = −(x − 2)2 + 5, identify the vertex, axis of symmetry, and y-intercept.
Vertex: (2,5)
Axis: x=2
y-intercept: f(0) = -(0-2)2 + 5 = -4 + 5 = 1 --> (0,1)
Simplify (4x² - 3x + 8) - (2x² - 5x - 3)
2x² + 2x + 11
Which direction do you shade (above or below) when graphing the inequality 2x - y < 4 after it is properly rewritten in slope-intercept form?
Above, (when isolated, it becomes y > 2x - 4)
Word problem: A phone plan charges a monthly base fee of $20 plus $0.10 per text. If Jamie's bill was $35, how many texts did Jamie send? Show the equation and the solution.
20 + 0.10t = 35 → 0.10t = 15 → t = 150 texts
Given two functions f(x) = 2x − 1 and g(x) = x2, find (f ∘ g)(2) and (g ∘ f)(2). Show steps.
(f ∘ g)(2) = f(g(2)) = f(4) = 2(4)−1 = 7
(g ∘ f)(2) = g(f(2)) = g(2·2−1) = g(3) = 32 = 9.
Simplify the expression (x - 2)(x² + 2x + 4)
x³ - 8
If you multiply the inequality -2 < x < 5 by -3, what is the correctly rewritten resulting compound inequality?
-15 < -3x < 6
OR
6 > -3x > -15