Calc-1 Discussion 01

Discussion Topics covered: Evaluating functions, composite functions, exponentials and natural logarithms, factoring, polynomial long division, conjugates

Part A: Review This Week's Lecture Topics (~30 mins)

Evaluating Functions

• Finding values for $f(a)$ given $f(x)$ and a value for $a$
• Finding expressions for $f(a)$ given $f(x)$ - leaving answer in terms of $a$
• Finding expressions for $f(a+h)$ given $f(x)$ - leaving answer in terms of $a$ and $h$
• Finding values for $f(g(a))$ given $f(x)$, $g(x)$, and a value for $a$
• Finding expressions for $f(g(x))$ given $f(x)$, $g(x)$

Exponentials and Logarithms

• Solving for $x$ in equations involving exponential functions such as $e^{x^2+1} = 6$
• Algebraic manipulation rules for exponentials (base $e$) and natural logarithms ($ln(x)$)

Part B: Next Week's Prerequisite Refresher (~30 mins)

Review the following prerequisite skills:

• Factoring second order polynomials (and the Quadratic Formula)
• Polynomial Long Division
• Multiplying a rational function involving radicals by their conjugate

Part C: General Q/A

Open the floor to questions from students regarding any topic