. Make a list of all 6 types of t and provide an exsmple for each one using the

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. Make a list of all 6 types of t and provide an exsmple for each one using the function )- 2. M513 Let ()()(-1),and () (+2)+1 (s). Suppose ala)-f(x)+&.What does o(2) equal? (b). Suppose the values of Ke) are twice as large as the corresponding valses of f(a). (a) Write g(a) in terma of f(x). Write an expression fore b(x) in terms of J(). ample: If 5, then k(a)--5). (b) Write A(a) In terms of f(e). (c) Draw g(x) and h(x) on the graph of (x). (e). Suppose all of the following transformation were done, in arder, to f(e) to get dx). Write an expression for d(a) in terms of f(). (). Shift left by 2, (u). Shift up by 3, (ii). Flip across -acis It may help to urite dom verbally all tranaformations (og a vertical/horisontal shif/stretoh/hip) done to get g) from ) and to get h(a) from (x). Draw g(x) on this graph. 5. M&I4;: #1 snd 2 (TO graph, you may want to use demos.) Draw h(r) to this graph. Label 2 points on h(r). Label 2 points on g(a). (a) What ? the vertex of f(s)? (b) Shift f() to the right by 3 to get g(x). Write an equation for q(x) (do not include 121 any other function ike f(z) in the equation). What is its vertex? (e) Stretch q(a) vertically by 2 to get r(z). Write an equation for r(x) (do not include any other function lkef(a) in the equation). What is its vertex? (d) Shift (z) down vertically by 5 to get s(a). Write an equation for s(z) (do not 43 2 10 include any other function lke f() in the equation). What is its vertex? 7. Let f(x)-2-1)2+32 (a). What is the vertex of f(x)? (b). On what intervals is f() concave up? Concave down? Neither? (c). Does f(a) attain a maximum? Does f(x) attain a minimum? Justify (d). Write f(z) in standard form. -12 (d) For g(z), what does (1,0) represent? How does the size of the vnlue of s(a) at r1 compare to the values of g(z) on either side of z 11? (e). What are the aeros of f(x). (). Write /(a) in factored form (e) For h(z), what does (-2, 1) represent? How does the vilue of h(x) at a-2 compare to the values of h(z) on either side of z -2? (f) What are the domain and range of (x)? Of g(r)? Of h(z)? 8. Give 3 different (equivalent) definitions of what it means for a general function f(x) to be concave down on an interval (a, b). (It may help to refer to class notes). (1) A visual definition (2). An analytie defiaition (Hint: Include average rate of change nat derieaties ) (3). A geometric definition

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