PreCalculus Review for Math 400

Transcription

1 PreCalculus Review for Math.) Completely factor..) For the function.) For the functions f ( ), evaluate ( ) f. f ( ) and g( ), find and simplify f ( g( )). Then, give the domain of f ( g( ))..) Solve. Write your solutions in eact, simplified form. 5.) Find the equation of a line that passes through (9, ) and (, 5). Put your answer in slope-intercept form..) State the domain of the function f( ) 5 using interval notation. 7.) State the range of the function.) Rationalize the denominator: f ( ) 5 5. using interval notation. 9.) Rationalize the numerator: 5..) Find the intersection points of the graphs of y and y..) Find the verte of 7. y.) Find the and y-intercepts of 9 y..) Simplify..) Solve y y y for. 5.) If f ( ), simplify f h f ( ) h.) What is the average rate of change of the function y on the interval [, 5]?

2 7.) Identify each of the following as a.) a function or.) a relation, ut not a function..) Which of the following is a polynomial function? Circle the correct answer. a.) y.) y c.) y sin d.) y e.) y e 9.) Find the two numers and y that satisfy y and have the greatest possile product..) If m, what is m?.) Match the formula to the graph y drawing lines. y y y y

3 .) Find the requested features of the function graphed elow. Use interval notation. a.) domain.) range.) Find the requested features of the function graphed elow. Use interval notation. a.) interval where it is increasing.) interval where it is decreasing.) Find the requested features of the function f graphed elow. a.) f ( ).) all such that f( )

4 5.) Find the requested features of the function f graphed elow. a.) the maimum value of the function.) the minimum value of the function.) Complete the identities. sin cos cot sec 7.) Complete the identities. sin sec tan.) Complete the identities. sin cos cos sin 9.) Complete the identities. cos sin sin y sin cos y.) Using the diagram elow, write the angle as a function of.

5 .) Lael each of the following functions as even, odd, or neither ) Find the sum:.) Solve sin. Find all solutions in the interval,..) What is the horizontal asymptote of the function y 5? 5.) What are the vertical asymptotes of the function y 5?.) What is the solution set of? 7.) Write down the formulas for finding the following geometric quantities. Volume of a Cone Volume of a Sphere Surface Area of Sphere Volume of a Cylinder Lateral Surface Area of a Cylinder Total Surface Area of a Cylinder Area of a Trapezoid Lateral Surface Area of a Cone Total Surface Area of a Cone.) Determine the slant asymptote of y 9 9 5

6 9.) Given that the two triangles elow are similar triangles, find the shortest side of the smaller triangle ) Solve algeraically:.) a.) Write an equation for the function elow that has the form y a sin( c) d.) Write an equation for the function elow that has the form y a cos( c) d

7 .) Give the domains and ranges of each of the following functions: a.) y sin ( ).) y cos ( ) c.) y tan ( ) d.) y sec ( ).) Find the distance etween the points (, -) and (-7, -9).) Suppose a and can e any real numers. Mark each of the equations elow as true or false. a a a a a a a a a a a a a a a a a 5.) Graph, f ( ), 5, 7

8 .) Graph f( ). Show any holes or asymptotes. 7.) Show that equals

9 Key for Review Sheet.) ()( 5).) -.) f( g( )) ; Dom( f g) (,) (,) (, ).) ) y 5 5.), 5 5, 7.), 5.) 5 9.) 7.) (, 9); (-, ).) (, -) 9.) (9, );,.) y.) y 5.).) 7 7.) a, a,,.) d 9.) = 5, y =.) m.) Match the formula to the graph. y y y y

10 .) [-5, ]; [-, ].) [-5, ]; [, ].) ; - and 9 5.) ; -.) 7.) sin cos ; sin ; sec ; csc cos cot csc ; tan sec cot tan sin.) tan cos cos ; cot sin 9.) sin sin cos ; cos cos ; sin y sin cos y sin ycos.) sin.) neither, odd, neither, even.).) 7,.) y 5.), 7 9.), 7.) Write down the formulas for finding the following geometric quantities. Volume of a Cone Volume of a Sphere.) y 9.).7 V r h Volume of a Cylinder V r h Area of a Trapezoid A h V r Lateral Surface Area of a Cylinder A rh Lateral Surface Area of a Cone A r r h Surface Area of Sphere V r Total Surface Area of a Cylinder A rh r Total Surface Area of a Cone A r r h r.) -, i.) a.) ysin.) y cos (other answers possile) (other answers possile)

11 .) Function Domain Range y sin ( ),, y cos ( ),, y tan ( ),, y sec ( ),,,,.) or..) a a False True a a True a a False a a False a a False a a True a a True a a a True 5.) Graph, f ( ), 5,

12 .) Graph f( ). Show any holes or asymptotes. 7.) Show that a) Factor the numerator: equals ) Simplify inside the rackets: c) Bring to the denominator and drop the negative: d) Rewrite the fractional eponent as a radical: