This problem set is a good representation of some of the key skills you should have when entering this course.

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Marcus Reed
5 years ago
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1 Math 4 Review of Previous Material: This problem set is a good representation of some of the key skills you should have when entering this course. Based on the course work leading up to Math 4, you should be able to make significant contributions to each of the problems. With limited review, you should be able to answer virtually all of the problems given. Use this document to help identify areas of weakness you might have and also to guide you in how to better prepare for the course. Here are some recommended resources: Algebra II tetbooks / Chapter of our tetbook. Notes and assignments from your previous courses. Khan Academy (online resource): Desmos (online graphing utility): YouTube: you know the address Searching may take time but there is a lot available. ) Key Vocabulary: These are terms that you should be able to define. You should also be able to provide eamples of each of these on graphs. Function / Vertical Line Test: Intercepts: One to one / Horizontal Line Test: Inverse of a Function: Domain/Range: Linear Function: Quadratic Function: Cubic Function: Radical Function: Rational Function: Eponential/Logarithmic Function: Constant Function: Roots (Zero product property) Slope / Intercept P a g e

2 ) Write an equation of a line with the indicated information: Slope = - and intercept = 4 Through the point (, -) with slope = - Through the points (, ) and (-, -) Through the point (, -) and slope = 0 Through the points (,0) and (, ) ) Graph each function. f g P a g e

3 4) Graph the inverse of f then find f graph by switching the and y coordinates.. Hint: Use the graph in the previous problem for the 5) Use the verte formula to find the verte (, y) of the quadratic function. Hint: b a f ( ) 6 6) Use interval notation indicate the solution to the following quadratic inequalities. Hint: Use test points. ( )( ) P a g e

4 7) Write the function for each graph: If the graph is eponential or logarithmic, base e must be used. Here are your choices: y, y, y, y e, y ln, y 8) Describe how the graph of each function is related to the graph of f(). Eamples: f( ) is shifted right units of f(). f(-) is rotated about the y ais of f(). f ( ) f ( ) f ( ) f ( ) f ( ) 4 P a g e

5 9) Sketch each graph on the grids provided. Hint: Use Desmos if you need help but you should be able to do these without help. y y ( 4) y ( ) y y ln y y y e 5 P a g e

6 0) Graph the following piecewise function. Refer to section. of our book for help. f : 0 : 0 ) Write each of the following epressions in the form Eamples: p where p is a real number. 5 4 = 5 = = 4 = 4 = = 4 = = 6 P a g e

7 ) Given the list of functions, answer the following. Use interval notation for the domain and range problems. Use Desmos if necessary for domain and range. 4 g 5 h f Domain of f. Range of f. Domain of g. Range of g. Domain of h. Range of h. f g f ( ) f f Evaluate and simplify f h f h Evaluate and simplify 7 P a g e

8 ) Write in logarithmic form. See section e 9 7 4) Evaluate each epression if possible. The solutions should not involve logarithmic epressions. See section.6. ln= ln e = ln 0 = log.0 = log 000 log 45 log7 7 = log9 7 ln e = 5) Solve each equation for such that there are no logarithms in your final answer. See section.6. log5 log 4 5 log 8 P a g e

9 6) Answer each true/false question. (Circle T for true or F for false.) If false, rewrite the right had side to make it a true statement. T F log 5 log5 log5 T F log 5 log 7) Solve each equation. Use natural logarithms (ln) only. Give eact answers (no calculators) P a g e

Calculus w/applications Prerequisite Packet Paint Branch High School Math Department

Calculus w/applications Prerequisite Packet Paint Branch High School Math Department Updated 6/014 The problems in this packet are designed to help you review topics from previous math courses that are important to your success in Calculus with Applications. It is important that you take