Fundamental Concepts in PreCalculus

📐The absolute value guarantees that everything is positive, ensuring that distances are never negative.

🧠The key to adding fractions is the common denominator, allowing you to add things of the same type.

📊Pascal's triangle gives you a way of organizing binomial coefficients, which represent the number of different ways to choose items out of a set.

📈A polynomial expression consists of powers of a variable and coefficients, with the degree of the polynomial being determined by the highest power of the variable.

🔢

📊The natural log is easier to deal with than logs to other bases in calculus, and understanding the natural log allows you to understand every other logarithm.

📐Understanding the relationship between angles and their corresponding first quadrant values makes trigonometry much more manageable and less intimidating for beginners.

📐The fundamental trig identities are the basis for deriving all other trigonometric identities, making them essential in calculus.

📈Most of the lines that you're going to encounter in calculus are going to be tangent lines.

📈Exponential functions grow faster than any other elementary functions, leading to exponential growth that gets very big very fast.

🔢Logarithms are defined as the inverse of exponential functions, answering the question of what exponent is needed to raise a base to a given power.

📈Calculus can help us find the exact location of where a graph bottoms out, filling in the details that we can't quite get just by looking at the zeros and the leading term.

📊Calculus can provide more precise information about the behavior of a function near asymptotes, such as whether it approaches a horizontal asymptote from above or below.