Algebra 2 and Pre Calculus Review Section 1: Sketch the graphs: 1 ...

Algebra 2 and Pre Calculus ReviewSection 1:Sketch the graphs:11. y x 32.2y 9 x3. y x 32214. y x 25. y 6. y xx 1Find the x and y – intercepts.7. y 2x 38. y x x 29. xy 42210. x y x 4y 0 11. y 2 x x 1 12. y x 4x22 23Check for symmetry with respect to both axes and the origin.13. y x2 214. y x x215. xy 416. y x x 3Sketch the graph of the equation. Identify any intercepts and test for symmetry.17. y x18. y x 319. y 3x 220. 1 y x 421.2y 1x22. y x3 2223. y x 2 2124. y xFind the points of intersection of the graphs of the equations; check the solutions.x y 22x y 6y x25.26.27.32x y 1x y 4y x28. Find the sales necessary to break even (R = C) for the given cost C =8650x+250,000 of x units and the given revenue R = 9950x obtained by selling xunits.

Algebra 2 and Pre Calculus ReviewSection 2:Plot the points and find the slope of the line passing though them.1. (3, - 4), (5, 2) 2. (1, 2), (- 2, 4)Find the slope and the y-intercept (if possible) of the line.3. x 5y 204. x 4Find an equation of the line that passes through the point and has the indicated slope.Sketch the line.Point Slope5. (0, 3)3m 46. (0, 0)2m 37. (0, 2) m 4Find the equation of the line that passes through the points, and sketch the line.8. (2, 1), (0, - 3) 9. (0, 0), (- 1, 3) 10. (1, - 2), (3, - 2)Write equations of the lines through the point (a) parallel to the given line and (b)perpendicular to the given line.Point Given Line Point Given Line11. (2, 1) 4x 2y 3 12. 7 3 , 8 4 5x 3y 013. (2, 5) x 414. Find a linear equation that expresses the relationship between the temperature indegrees Celsius C and the temperature in degrees Fahrenheit F. Use the factthat water freezes at 0°C (32°F) and boils at 100°C (212°F). Use the equation toconvert 72°F to degrees Celsius.

Algebra 2 and Pre Calculus ReviewSection 3:Evaluate (if possible) the function at the specified value(s) of the independent variableand simplify the results.1. f ( x) 2x 3a) f (0)b) f (3)c) f (b)d) f ( x 1)2. f ( x) x 3a) f (2)b) f (6)c) f (c)d) f ( x x)3.2x1,x 0f ( x) 2x 2, x 0a) f (1)b) f (0)c) f (2)d) f ( t2 1)4. f ( x)xx15.f ( x) x23f (2 x) f (2)xf ( x x) f ( x)xFind the domain and range of the given function.6. f ( x) 4 x7. f ( x) x 28.2f ( x)9 x 9. f ( x) x 2Determine whether y is a function of x.2210. x y 411. x y 422212. y x 113. x y x 4y 022

14. An open box of maximum volume is to be made from a piece of material 24centimeters by 36 centimeters by cutting equal squares from the corners and turning upthe sides.a. Fill in the table below. The first two rows are completed.Height,xLength,lwidth,wvolume,V124 2(1) 2236 2(1)341[(24 2(1)(36 2(1)] 748224 2(2) 2036 2(2) 322[(24 2(2))(36 2(2))] 12803456b. Write the volume as a function of x, the length of the corner squares. What is thedomain of the function?c. Use a graphing utility to graph the volume function and approximate thedimensions of the box that yield a maximum volume.

Algebra 2 and Pre Calculus ReviewSection 4:Find the inverse function of f. Graph (by hand) f andbetween the graphs.1. f ( x) 2x 32.3. f ( x) x4.f1. Describe the relationshipf ( x) x52f ( x) 4 x x 0Find the inverse function of f. Use a graphing utility to graph f andviewing window. Describe the relationship between the graphs.1f in the same5.( x)3x 1f 6.2 3f ( x) xx 07. Temperature The formula F 325C , where F 459. 6 , represents the9Celsius temperature C as a function of the Fahrenheit temperature F.(a) Find the inverse function of C.(b) What does the inverse function represent?(c) Determine the domain of the inverse function.(d) The temperature is 22°C. What is the corresponding temperature in degreesFahrenheit?Evaluate, in RADIANS, the expression without using a calculator.18. arcsin 9. arcsin 0210.3arctan 11.3 3arccos 2 Use a calculator to approximate the value. Round your RADIAN answer to threedecimal places.12. arccos( 0.8)13. 0.39)arcsin( 14. arctan3