Piecewise Functions Quiz Review

Transcription

1 Piecewise Functions Quiz Review The review packet is designed to get ready for this week s quiz. You should complete the problems independently in class and treat it as though it is a quiz (time yourself efficiency is always key). However, I encourage you to refer to your classnotes if you get stuck. For questions you absolutely cannot answer, circle them and we will review them on Thursday. Both sections will take the quiz on Friday, //07 unless you have made alternative arrangements with me and notified me of your absence on Friday. The completed packet will be collected and graded for both HW and CW credit, due Friday, //07. By completing this packet, you are also preparing for your quiz! Since composite functions were not included on the last quiz, you will see them on this quiz. Topics covered: o Composite Functions o Linear piecewise functions (interpreting and graphing) o Absolute Value Functions (Solving equations, solving inequalities, using tolerance, identifying vertex, graphing functions) I. Composite Functions ) For the given functions f ( x) = x ; g( x) = x, find: (HINT: You must evaluate one function at a time. The output from the first function is the input for the second function. Remember to FOIL when multiplying two binomials) (a) ( f g)() (b) ( g f)( 4) (c) ( f f)( ) (d) ( g g)( 6) (e) ( f g)( x ) = (f) ( g f)(4 x ) = (g) f f x = (h) ( g g)( x) = ( )( ) a) g( f( 5)) = ) Evaluate the following: f ( x) = x+ gx ( ) = 5x 5 f x x x ( ) = gx x x b) g( f( x )) = ( ) = f x x x gx ( ) = x c) f( g( x )) = ( ) = 7 9

2 II. Piecewise Functions ) Graph the following piecewise functions. (HINT: Graph each piece as though it were a line and just darken the piece that pertains to the domain. Use y = mx+ b for more efficient graphing. Alternatively, you can make a table but its more work. Remember that inequalities with a < or > sign are open circles. For inequalities with a or sign, use a closed circle. Piecewise functions MUST NOT criss cross each other. Please use a ruler!) x 8, if x< 9 x +, if x < a) f( x) = b) f( x) = x 4, if x x, if x 9 c) x 4, if x< f ( x) = x+, if x< x +, ifx d), if x < 0 f( x) = x+, if 0 x< x 4, if x

3 ) At Pace University, students are allotted 0 free pages of printing per week. After that, they pay $.0 a sheet for each page up to 40 pages, $.07 a sheet for each page up to 70 pages, and $.05 for each page after that. Using this information, a) How much would it cost to print 5 pages? 5? 65? b) Write a function f ( x ) of that variable which represents the cost to the student for printing x pages in a given week. f( x) = c) Test to make sure your function works: Do you values for f (5), f (5) and f (65) work for your function in (b)? d) Graph your function below for x 0, y 0. III. Absolute Value Functions ) Solve and check the following absolute value equations: a) 6 x = 9

4 b) x + 4 = 0 c) 0 6x = 6 d) x 5 + 0= 8 e) x = 9 f) x+ = x 4

5 ) Solve and check the following absolute value inequalities: a) x + 5 b) x + 4 > c) x + < 6 d) x e) 6< x + < 8

6 Tolerance Applications: Remember to use the tolerance inequality: Actual Ideal Tolerance ) The ideal diameter of a certain type of a spindle is 0 millimeters. The manufacturer has a tolerance of millimeter. a)write an absolute value inequality that describes the acceptable diameters for these spindles. b) Solve the inequality to find the range of acceptable diameters. 4) If manufactured correctly, a basketball should bounce from 48 inches to 56 inches when dropped from a height of 6 feet. Write an absolute value inequality that describes the tolerance for acceptable bounce heights. Absolute Value Graphs: Remember that an absolute value function is represented by the vertex form: y = a x h + k. a, h, and k all affect where the graph lies. Use a ruler please! ) For each of the following absolute value functions below, identify the following and graph them below: Equation f (x) = x 4 + f ( x ) = x+ f (x) = x a = Vertex: (h,k) Opens Up/ Down: Wider/ Narrower/ Same as y = x x- intercepts (when y =0)

7 Equation f( x) = x+ f( x) = x+ a = f( x) = x + Vertex: (h,k) Opens Up/ Down: Wider/ Narrower/ Same as y = x x- intercepts (when y =0) ) A rainstorm begins as a drizzle, builds up to a heavy rain, and then drops back to a drizzle. The rate r (in inches per hour) at which it rains is given by the function r = 0.5 t where t is the time (in hours). a) Graph the function. b) For how long does it rain and when does it rain the hardest?

8 ) For each of the following absolute value equations below, identify the corresponding x-value for the given y-value. Keep responses in fractions! Equation y = x + 5 y = x Corresponding x- value(s): y = x+ 5 y = 4 y = y = 5 y = 4 y = x + 6 Case : Case : Case : Case : 4) Write an equation each of the six graphs shown below (HINT: Start with the vertex and use the other given point to find slope and place in y = mx + b form ): Vertex: Vertex: Vertex: Slope: Slope: Slope: Y-intercept: Y-intercept: Y-intercept: Equation: Equation: Equation: