Review Midterm 1 •
The midterm will cover sections 1.6, 1.9, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, and 3.1. •
You will have 80 minutes to take the exam in class on January 29th. •
You will be allowed to use 3x5 index card with hand written notes on both sides. Make sure it is truly a 3x5 index card and not something that closely resembles a 3x5 index card. •
You will NOT be allowed to use a calculator (or other electronics), notes, textbook, or your neighbor. •
You must show your work to receive credit. (You work should be organized and legible.) •
Scratch paper will be provided; scratch work will not be graded. •
Bring your student ID and a pencil & eraser. You should be able to… •
Functions: o Identify whether a relation is a function. o Identify whether a function is a 1-­‐to-­‐1 function. o Identify the domain and range of a function. o Find the x-­‐intercept(s) and y-­‐intercept of a function. o Identify whether a function is even, odd, or neither. o Identify when a function is increasing and decreasing. o Identify turning points of a function. o Use function notation to evaluate a function. o Add, subtract, multiply, and divide functions. o Find the composition of two functions. o Given a function is composed of functions, identify the functions. o Find the difference quotient. •
Sketch each of the function in our “Library of functions”. o Identity o Absolute Value o Quadratic (Square) o Cubic o Square Root o Cube Root o Reciprocal o Greatest Integer Function •
Identify shifts, stretch/shrink, or reflections of a function. •
Use transformations to sketch the graph of a function. •
Write the equation of a transformation of a function from our “Library of fn.” •
Understand piecewise functions. o Domain & Range o Evaluate o Sketch Graph •
Identify when a function has an inverse. •
Algebraically verify that two functions are inverses. •
Find the inverse of a function. •
Solve absolute value equations •
Solve absolute value inequalities. •
Solve nonlinear inequalities. •
Calculate the slope of a line given 2 points. •
Calculate average rate of change. •
Calculate the slope of a secant line. •
Calculate the slope of the tangent line. •
Write the equation of a line. •
Write the equation of the tangent line to a function at a given point. •
Write the equation of the normal line to a function at a given point. Practice Problems: Ch. 1: p. 72 (Self-­‐Test) #5, 6, 8, 9 p. 72-­‐73 (Practice for Calculus) #6, 16, 22, 24, 28, 36, 39-­‐49odd, 52, 55, 56-­‐59 Ch. 2: p. 152-­‐153 (Self-­‐Test) #1, 2, 4, 5abce, 6, 7bcde, 8, 9, 10 p. 153-­‐154 (Practice for Calculus) #5-­‐12all, 13-­‐29odd, 33-­‐44all, 53-­‐57odd Ch. 3: p.167-­‐169 #6, 10, 12, 16, 22, 24, 28, 36, 52