Test review key PA algebra 2.pdf

Honors Algebra 2 – PA TEST Review Name: ________________ A. Solving Equations & Inequalities: 1. 1 ( 4 x + 10 ) = 5 - 3x 2. 1 2 a+ =a-...

Honors Algebra 2 – PA TEST Review Name: ________________ A. Solving Equations & Inequalities: 1. 1 ( 4 x + 10 ) = 5 - 3x 2. 1 2 a+ =a- 3 3. 5x - 2 ( 3 - x ) = - ( 4 - x ) 2 2 3 4 5 5 9 55 6 8 120 9 6712 14 4 129 8 69 17 a ! 4. -2 < 2 x - 1 < 3 5. " ! + 6 ≥ −3(! − 1) 1 Éfg 1 2 24 220 12 Imme cosmmm 1 2,2 Interval notation: ________________ EET Interval notation: ________________ EEF or É Loom LIFE is 15 OR fund 843mn03 2 5,0 3,75 3 XD 5  the number ofticket qgx to 265 34.95 4 255 x 7.29 onlyenough for to 7 people go B. Which Variable to Solve for ? 6. 1 3 5 x + y = 6 (for x) 7. 3 x = 4 xy - 10 (for x). 8. C = ( F - 32) (for F) 2 5 9 5 69 60 SEE EYE 91 32 7 5 ÉY 2A 2 b.t bits x 2f bz b 9. V=r^2*h is an equation to calculate the volume of a cylinder, V, where r represents the radius of the cylinder and h represents its height. 4 10.  C. Relations, Functions, Domain & Range 1) For the given relation, convert to the speci4ied form. Start (Mapping Diagram) Table Graph on 0 0 1 2 2 3 5 4 a) Is the relation a function? (Yes or No) Why or why not? 0,112,530 b) State the Domain:________________ c) State the Range:________________ 0,3314 Which of the following are functions? State the domain & range Domain: 852,143Domain: 567,8 Domain: 1 Range: 10,9103 Range: 9 319 3 Range: 4,915,0 Domain: 5,3 Domain: too Domain: 3,0 2,4 5 51,43 Range: Range: Range: 1,7 6,0 Given the graph for f(x) find the following: a. f(-3) 5 b. f(0.5) 3 c. What is x if f(x) = -2? 3 If !(#) = 3# + 4 and )(#) = # ! + 5# − 3 Find the following: a. !(2) 3 L b. )(2) 415 c. )(−1) d. !(−1) 4 54 Find the value of x that makes the equation true. 34 44 a. f(x) = 10 b. f(x) = -1 10 3 4 1 3 4 6 34 s  3 D. Moving Function/Reflection/Outputs & Parent Functions Here is a graph of *(!) = √! and a graph of -, which is a transformation of *. Write an equation for the function -. x F 2 g I Describe the transformation that takes the graph of function * to the graph of function -. a) *(!) = √! and -(!) = √! + 3.5 left 3.5 b) *(!) = |!| and -(!) = |−! − 2| + 4 reflects 4the y axis shifts up c) *(!) = 2# and -(!) = 2$# − 1 reflects the y axis shifts down I d) *(!) = ! % and -(!) = −(! − 1)% − 5 resf right Iowns Start with f (x). Write the function notation for a function that is reflected over the x-axis, horizontally shifted 1 unit right, and vertically shifted 2 units up. Fx f ___________________ x 1 2 Start with f (x). Write the function notation for a function that has a vertical stretch by a factor of 3, horizontal shift 4 units right and vertical shift 1 unit down. F x 3fx _____________________ 4 1  21 3 5 FA 1 2 FA 5 4 f  subtyver 4 41 1 2 C 90 3,0 PP 2,0 IE I 4 Eap Go 4J old 0,5 to.es 0,3 40,0 0,0 for o 0,3 4,0 0,0  E. Piecewise: Evaluate the function for the given value of x. ! 3# − 7, +! # ≤ 2 3# + 5, +! # < 5 # + 1, +! # > −3 !(#) = & 1(#) = & ℎ(#) = 7" 6 − 2#, +! # > 2 −# + 3, +! # ≥ 5 2# − 3, +! # ≤ −3 1. !(0) 2. !(−3) 3. 1(5) 4. 1(−4) 5. ℎ(−9) 6. ℎ(−3) 1 - I 34 29 EEF f(x) 5 y Write the equation for the piecewise function. 4 i Remember to include the domain restrictions. 3 2 1 x ⬚ -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 *(!) = 3⬚ -1 -2 ⬚ Write the equation for the piecewise function. f(x) Remember to include the domain restrictions. 5 y 4 3 ⬚ 1 2 *(!) = 3⬚ 1 ⬚ x -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -1 -2 Graph them both on one grid. (Make sure your function passes the VLT) 3, 8* ! ≤ 4 −|! + 2| + 2, 8* ! ≤ −1 *(!) = 5 *(!) = 5 −1, 8* ! > 4 !& − 2 , 8* ! > −1 for.it t a o 2|!| − 3, 8* ! < 1 (! − 1)! − 3, 8* ! ≤ 2 *(!) = 5 *(!) = < 2 , 8* ! ≥ 1 √! − 2 + 1, 8* ! > 2 r a got if ! − ! − 2, 8* ! ≤ 0 |! − 1| − 1, 8* ! > 0 *(!) = < & *(!) = 5 (! − 2)& + 2, 8* ! > 0 −2√! , 8* ! ≤ 0 0 O t an  F. Absolute Value Equations & Inequalities Solve each of the following equations or inequalities, then graph their solutions when necessary. Check for any extraneous solutions. Inequality answers should be given in interval and inequality notation as well as graphed on the number line for all inequalities. 924 1034 9 24 10 4 357 ÉÉ Eyes EEEE p t.EE I iEEi mtg kin alibaba.az to v o G. Application 1. Here is the graph of a function *. b. Write an equation (in terms of *) for a function - that has the graph that you drew. 3 go gEx a. On the same axis, sketch a graph of * 947 4 5 3 reflected over the >-axis and then translate it 3 units up. 1 35 1 9 6 35 1 2. Here is the graph of > = *(!) for a cubic function *. 2 a x h K b it it IÉEan a a. Will scaling the outputs of * change the !-intercepts of the graph? Explain how you know. No because the y 8 15 effected it since its zero won't change a b. Will scaling the outputs of * change the >-intercept of the graph? Explain how you know. yes because the y valuenot zero is a number Hangers therefore it will change In this hanger, the weight of the triangle is ! and the weight of the square is >. a. Write an equation using ! and > to represent the hanger. 4 By 4 2y 3x b. If ! is 6, what is >? 18 2y  y 3. Here is a balanced hanger diagram. Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and ! represents the weight of each square. Select all equations that represent the hanger. 2 s XtX 2.5 9 Xtxtx 2.5 2.5 3 3 0 3 X 4 11 2 11.5 2x 65 a. ! + ! + ! + ! + 11 = ! + 11.5 b. 2! = 0.5 c. 4! + 5 + 6 = 2! + 2.5 + 6 Od. 2! + 2.5 = 3 O e. 4! + 2.5 + 2.5 + 3 + 3 = 2! + 2.5 + 3 + 3 + 3