Chapter.Section Objective and Example Material covered byEnd of week number:1.11.1, 1.2, 1.3, 1.4Given a linear, quadratic, or simple rational function the student will be able to calculate the Difference Quotient.Example:Calculate the Difference Quotient for1f (x)x=.Given a graph or equation, the student will be able to discuss and manipulate the salient features and properties of it using appropriate vocabulary and sketching if needed.Example:Given the following graph, answer the questions below:Is this a function? How do you know?What is the domain? the range?Is it a 1:1 function? How do you know?If it is 1:1, give a formula for the inverse function. Sketch the inverse function.Where are the intercepts?Where is the graph increasing? decreasing?Are there any symmetries? Be specific.Sketch the graph of f (2 x)- -; show important points on this shifted graph.# 1# 2Math 1330 Course Objectives1Chapter.Section Objective and Example Material covered byEnd of week number:2.1, 2.2, 2.32.4Given the equation of linear function, a rational function, or a polynomial or adequate information about the function, the student will be able to use sketching techniques and algebra to graph the function and label the sketch appropriately.Examples:Sketch and label the graphs of the following functions:1. the linear equation with an x-intercept of5 and having an x-intercept of 3 on it’s inverse.2. 2f (x) 3x 6x 1=- + -3. this function has degree 4 and zeros i, 5,and -1.4. 3 2f (x) x 6x 5x=- + +5. 22x 4x 3f (x)x 2x 3+ +=- -Given a word problem, the student will beable to customize a governing equation and solve for the missing quantity if requested.Example:A rectangle is inscribed above the x axis andinside 2f (x) 25 x= -. What is the formula for the area of the rectangle? for the perimeter of the rectangle?#4#4Chapter. Section Objective and Example Material covered byEnd of week number:23.1, 3.23.33.4Given the graph of an exponential function or a logarithmic function, the student will be able graph it, label key features, and calculate points that are on the graph.Examples:1. x 1f (x) 4 64-=- -2. 7f (x) log (x 49) 1= - -For these equations:Graph. Calculate the intercepts. Discuss where the graphs are increasing or decreasing. Give the domain and range.Calculate f(3) for 1. and f(98) for 2. The student will be comfortable applyingthe Laws of Logarithms.Example:Rewrite the following as a single logarithm:2 2log (x 3) log (x 5) 1+ - - +The student will be able to solve equations with logarithms or exponentials.Examples:Solve for x1. 4 4log (x) log (x 6) 2+ + =2. 2 x2739-=#5#6#63Chapter. Section Objective and Example Material covered byEnd of week number:4.1, 4.2, 4.3 The student will be able to find the trigonometric function values of an angle presented in a triangle with side lengths given. The student will be able to calculate trigonometric function values for angles related to the standard angles in Quadrant 1. Examples:1. Find thetrigonometricfunction values for A. 2. Find thetrigonometric function values for 54pq=.3. Find the trigonometric function values for q, given that 2 3cos , 27 2pq= <q< p.The student will be competent at verifying trigonometric identities.Example:Verify the identity:tan tan2cscsec 1 sec 1q q+ = qq- q+#84A13"12 "Chapter. Section Objective and Example Material covered byEnd of week number:5.15.2, 5.35.4The student will be aware of the properties of the trigonometric functions including but not limited to even/odd and periodicity.Example:Simplify sin( t 46 )tan(13 t)- + pp-The student will be able to graph and discuss salient features for all the trigonometric functions.Examples:Graph and label the important features:1. f (x) 2sin(5x )4p=- +2. f (x) sec(2x)=The student will be able to perform calculations involving inverse trigonometric functions and will be able to graph the inverse trigonometric functions for sine, cosine, and tangent.Examples:1. 13cos(sin ( ))7-=2. Graph 1f ( ) tan ( )-q = q. Label the intercepts and list the domain and range.#9#10#105Chapter. Section Objective and Example Material covered byEnd of week number:6.1, 6.26.3The student will be competent in applyingthe sum and difference formulas and boththe double angle and the half angle formulas.Examples:5cos( )12sin(75 )7sin( )8p==p=oThe student will be able to solve trigonometric equations on a restricted orunrestricted domain.Examples:1. Solve for x in the interval [0, 2p), 2sin x 3- =2. Find all solutions: 2cos x 1=#11#126Chapter. Section Objective and Example Material covered byEnd of week number:7.1, 7.2, 7.3 The student will be able to solve right triangles, use the trigonometric form of the area of a triangle formula and use the Law of Sines and the Law of Cosines on arbitrary triangles competently.Examples:1. Find the lengths of the legs.60cm302. Find the length of the shortest side.x10 cm30453. Find the area and the missing length.9"5"120#137Chapter. Section Objective and Example Material covered byEnd of week number:8.18.28.3Given an equation or a well-labeled graph, the student will be able to identify the focus and the directrix of the parabola.Example:Give the focus and the directrix for the cupped up parabola whose x-intercepts are 3 and 5.Given an equation or a well-labeled graph, the student will be able to identify the foci, axes and their lengths, the center,and the vertices of the ellipse. Example:Give the key features of the ellipse:2 24(x 1) 25y 100- + =Given an equation or a well-labeled graph, the student will be able to identify the foci, axes, the equations for the asymptote lines, the center, and the vertices of the hyperbola. Example:Give the key features of the hyperbola:2 2(x 2) (y 1)149 25- +-