May, 2025 Instructions: Answer the questions clearly. No calculators, books, or notes. Show all work. Formulas: $$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

How to find what $x$ makes a polynomial or rational function positive or negative? Example. Solve $(x+4)(x-3)<0$. Root Behavior: Factor Zero Multiplicity Bounce or cross $(x+4)$

Current Topic 4.5 - Vertical and Horizontal Asymptotes, Graphing Rational Functions Chapter 1 Arithmetic Review (need to finish) 1.1 - Graphing, Intercepts, Distance, Midpoint (need to finish) 1.2 - Functions 1.3 - Slope Practice Exam 1 1.4 - Parallel and Perpendicular Lines

Glossary of Key Terms Simplify: To rewrite an expression in a less complex form, typically by combining like terms, canceling common factors, or performing operations. Common Denominator: A denominator that is the same for two or more fractions, allowing them to be added or subtracted. The least common denominator (LCD) is the smallest such denominator. Distribute: To multiply a factor across all terms within a set of parentheses, e.g., $a(b + c) = ab + ac$. Combine Like Terms: To add or subtract terms that have the same variable raised to the same power. Isolate the Variable: To manipulate an equation using algebraic operations so that the variable you are solving for is alone on one side of the equation. Function Division ($(g/f)(x)$): An operation on two functions where the result is a new function whose value at any point $x$ is the quotient of the values of the two original functions at that point: $\frac{g(x)}{f(x)}$. Function Composition ($(f \circ g)(x)$): An operation where one function is applied to the result of another function. $(f \circ g)(x) = f(g(x))$. Outside Function: In a composite function $f(g(x))$, the function $f$ that is applied to the result of the inside function.

Spring, April 2025 Exam 3 is on April 25, 2025 in ACD 319 from 830-920am. Answer the questions clearly.No calculators, books or notes. Show all work. 1. Simplify. a. $\dfrac{\left(\tfrac{4}{3}\right)}{-7}=$ Solution: Step

Spring, April 2025 Exam 3 is on April 25, 2025 in ACD 319 from 830-920am. Answer the questions clearly.No calculators, books or notes. Show all work. 1. Simplify. a. $\dfrac{\left(\tfrac{4}{3}\right)}{-7}=$ Solution: Step

Goal: Draw a rough graph of polynomial function. We will take into account (1) the leading term test and (2) plot intercepts. Key fact with $x$ intercepts: if the multiplicity is odd, the graph crosses the axis. If the multiplicity is even, the graph bounces off the axis. Even Multiplicity (Bounce off x-axis) Odd Multiplicity (Pass through x-axis) image image

November, 2024 Answer the questions clearly.No calculators, books or notes. Show all work. 1. Solve the equation: $$2(2x+1)-3(-x+5)=4(3x-1)$$ Solution: \begin{align}

Radical Equations Radical Equations. (These equations involve $\sqrt{\cdots}$ or $\sqrt[n]{\cdots}$) Basic principle: If $\sqrt{X}=a$, then $X=a^2$. We can see this as 'squaring both sides': if $$\sqrt{X}=a$$ then $$(\sqrt{X})^2=a^2$$ $$X=a^2$$

Quadratic functions: $3x^2 - 2x + 4$ $-4x^2 + 3x + 1$ $5x^2 - 2x$ (this is $5x^2 - 2x + 0$) $-2x^2 + 4$ (this is $-2x^2 + 0x + 4$)

December, 2024 Instructions: Answer the questions clearly. No calculators, books, or notes. Show all work. Formulas: $$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

Number Factors 1 1 2 1, 2 3

Exam Study Ritual: For each problem: Write and speak each problem and solution out loud. Come up with notes to write to your future self to help you remember how to do that particular problem. Be able to write and generate your own correct solution from scratch without looking at the solutions. Make flash cards where the front is the question and the back is the solution. Look at every flash card multiple times every day. In general:

1.6 Linear inequalities. Rules for solving similar to those of linear equations, with one exception: if you multiply or divide an inequality by a negative number, the inequality reverses. Example. If $$ 2x < 5 $$then$$ x < \frac{5}{2}. $$ Example. If$$ -2x < 5 $$then$$ x > -\frac{5}{2}. $$ Example 1. Solve $$4x-1>7x-8$$ Step

$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ $$\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$$ $$m=\dfrac{y_2-y_1}{x_2-x_1}$$

Front Door – Fraction Fun Screenshot 2025-02-17 075900 Theme: A giant door painted with pizza slices. Key Concepts:Multiplying Fractions (Multiply straight across):Imagine the pizza slices being combined $$\frac{3}{7} \times \left(-\frac{5}{2}\right) = -\frac{15}{14}$$ Subtracting Fractions (Need LCD to combine):Picture subtracting toppings : $$\frac{1}{4} - \frac{2}{3} = -\frac{5}{12}$$ Entry Hall – Order of Operations (PEMDAS)

Instructions Answer the questions clearly. No calculators, books, or notes. Show all work. Formulas $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ $$\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$$ $$m=\dfrac{y_2-y_1}{x_2-x_1}$$

Adding Two negative numbers: $$-5 - 26 = ?$$ First add the associated positives ('absolute values'): $$5 + 26 = 31$$ Final answer has a negative: $$-5 - 26 = -31$$

Chapter 1 Arithmetic Review (need to finish) 1.1 - Graphing, Intercepts, Distance, Midpoint (need to finish) 1.2 - Functions 1.3 - Slope 1.4 - Parallel and Perpendicular Lines 1.5 - Solving Equations 1.6 - Solving Inequalities Chapter 2

Graphing in the $xy$ plane. image Horizontal line across middle is called the x axis. Vertical line in the middle is called the y axis. They meet at the origin. Points in the plane are labeled with an ordered pair $(x, y)$. image