From Chapter 1 (1.1, 1.2 & 1.3)

1. What is a function, domain and range are.

2. How to identify the graph of a function from VLT (Vertical Line Test)

3. x-intercepts and y-intercept of a graph

4. Cost and revenue can be written (sometimes) as functions of number of items

5. Profit is revenue minus cost (Examples)

6. Break-even point of the point where profit =0 (So, revenue = cost). (Example)

7. Demand and supply can be written as functions of price

8. So (sometimes) we can also write cost and revenue also as functions of price. In both cases
   revenue = demand * price
   cost = fixed cost+ demand * price (We saw one example only on section 2.1) (Example)

9. In a linear function when x is changing by a fixed amount y values also changes by a fixed amount (Example)

10. How to find equation of a line, when:

    • Y-intercept (initial value) and slope is known

    • Two points on the line is given (Example)

    • A point and the slope is given (Example)

11. Using calculator to find the equation of a line that best fits given data (Linear Regression)
     

From Chapter 2 (2.1, 2.2 & 2.3)

1. Quadratic functions are of the form

2. The orientation of the quadratic function is determined by the leading coefficient

3. Quadratic formula  (Example)

4. Using you calculator to find the quadratic function that fits given three points (quadratic Regression) (Example)

5. Vertex formula (minimum and maximum of a quadratic function) (Example)

6. Exponential functions are of the form

7. While linear functions change by constant quantity, the exponential functions maintain a constant ratio of change.

8. There are 4 types of graphs of exponential functions (depending on A and b above)

9. How to find exponential functions, when

   • A growth/decay percentage is given (Example)

   • Two points on the graph is given

     • Initial point and one more (Example)

     • None of the two points are the initial point (Example)

   • Modeling compound interest (not covered on videos. Can be found on page 63 and page 144 of the textbook). (Example)

10. Finding exponential function that best fits given data, from calculator. (Exponential regression)

11. Using logarithm to solve for the exponent (power) in an exponential function. (Example)

12. Using calculator to find the equation of a parabola that best fits given data (Quadratic Regression) (Example)
     

From Chapter 3 (3.1, 3.2, 3.3)

1. Understand the concept of limits and the two-sided limits

2. Know that the limit is said to exists if and only if the two-sided limits exists and are equal.

3. Be able to find limits from a graph (Examples)

4. Be able to estimate limits using numerical methods

   • Finding two sided limits (Examples)

   • Recognize when the limit is approaching infinity (Example)

   • Find limits at either of the infinities (Example)

5. Understand what a continuous function is.
   We look continuity on the domain and on the entire real line. In each case the question needs to specify, if the question is asking for continuity in general or continuity on the domain

6. Understand what a closed form function is

7. To find limit of a closed-form function at a point on the domain we can just plug-in the value (Examples)

8. Limit at a point not on the domain

   • 0/0 form: Need to factor, cancel out common factors and plug-in (Examples)

   • K/0 form: Need to numerically check two sided limits. These two-sided limits could go to infinity or -infinity. Then check if the two-sided limits agree (Examples)

9. Limits at infinity (Examples)
    

Formulas that you may need to have written down

1. Profit = Revenue – Cost

2. Revenue (as a function of # of items) = Price * Items

3. Cost (as a function of # of items) = Fixed Cost + Cost per item* Items 

4. Revenue (as a function of price) = Demand * Price

5. Cost (as a function of price) = Fixed Cost + Demand * Price 

6. Slope-intercept formula of a line

7. Equation of a line passing through two point

8. Equation of a line with given a point and the slope

9. Quadratic formula

10. Vertex formula for a quadratic function

11. Compound interest formulas (here)

    • Compounded “n” number of times per year

    • Compounded continuously

12. Certain exponential and logarithmic formulas (algebra) (Stuff here & here)