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Calculus AB Name ________________________Summer Review ProblemsFor this course, you will need to know the following:How to graph equationsFactor, combine, simplify, rearrange algebraic expressionsInverse FunctionsTrigonometric ratiosTrig values at special anglesTrig identities (Pythagorean, Double Angle)LogarithmsLaws of exponentsLaws of logsLaws of ln and eFormulas from GeometryWork neatly! If I can’t read it, I won’t grade it. Show all work on a separate sheet of paper and “box” your final answer! You may only use a calculator when indicated. This is a grade and is due on the FIRST day of class. LATE WORK WILL NOT BE ACCEPTED. Using the table of values given above, find the average rate of change for f on the interval (2, 5) and write an equation for the secant line passing through the corresponding points.x0123456f(x)-10-8-10572Find the equation of the line that passes through (2, -1) and is perpendicular to the line 2x-3y=5.Create a “Parent Functions Cheat Sheet” by graphing all of the following parent functions on a single piece of graph paper: (You may use a graphing calculator, if needed)fx=xe. fx=3xi. fx=exm. fx=tanxfx=x2f. fx=|x|j. fx=lnxn. fx=secxfx=x3g. fx=1xk. fx=sinxo. fx=sin-1xfx=xh. fx=1x2l. fx=cosxp. fx=tan-1xGraph y=2xx-4. Label x- and y- intercepts and all vertical and horizontal asymptotes.Suppose fx=x-1, if x<2x-1, if x>2. Answer the following:f-3=f2=f10=Graph f(x)If fx=xx-1 and gx=1x-1, find f°g(x) and g°f(x).Solve the following4t3-12t2+8t=03x-2-8=82ln3x=4x-53-x≥02-x3<54e2x=52sin2x=sinx+1;0≤x≤2π Factor the following expressions:3x3+1922x3-11x2+12x+99x2-3x-2Simplify:2lnx-3+lnx+2-6lnx2x-31-1x-1x1-2x-32+1-2x12e-xe3-e3exe4xSimplify the expression x21+x2 using long division.Find the conjugate for the following radical expressions. Then use it to simplify the expression. (Yes we do sometimes conjugate the numerator in calculus)xx-x-13+x-3xFind the distance between 12, -7;(-3, 4)Find all the zeros of the following functions:y=sinxy=secxy=tanxy=cos2xFind the following:sin7π6cos120°tanπ2csc60°sec-2π3cot(-135)°Simplify the following trigonometric expressions: (trig identities)4sin2xcos2x1-sec2x1+cos2x2cos2x-sin2xcos2x+sin2x What do the following terms mean and give an example?Inverse of a FunctionEven FunctionOdd FunctionContinuous FunctionMaximum/Minimum Value of a FunctionRoots/Zeroes of a Function ................
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