Parent, Piecewise, and Transformed Functions
 ● Parent Functions◌ Piecewise Functions◌ Transforming functions Click then drag the equation by the description.Absolute value functionConstant functionCubic functionCube root functionExponential functionGreatest Integer functionIdentity functionlog base b functionQuadratic functionReciprocal functionSquare root functiony=logb(x)?y=[x] or y=int(x,1)?y=|x|?y=x3?y=∛x?y=bx?y=1?y=√x?y=1/x?y=x2?y=x? f(x)x-202Equation:Domain: xεRange: f(x) εParent Functionf(x) = (-∞,∞)? {1}? f(x)x-101Equation:Domain: xεRange:a.k.a.Identity function?Parent Functionf(x) ={f(x) εℛ }?(-∞,∞)? f(x)x-2-1012Equation:Domain: xεRange: f(x) εa.k.a.Square function?parent functionf(x) =(-∞,∞)?[0,∞)? f(x)x-1-1?-⅛?-½00?⅛?½11?8?2Equation:Domain: Range:parent functionf(x) =f(x) ε (-∞,∞)?x ε (-∞,∞)? f(x)x-44?-22?00?1?133?5?5parent functionEquation:Domain: xεRange: f(x) εf(x) ={f(x) =-x,x,(-∞,∞)?[0,∞)?x<0?x≥0? f(x)x-2.5-3?-1-1?0?01.81?3?3Eq:parent functionDomain: xεRange: f(x) ε Rounds upRounds downa.k.a.Greatest Integer Function?f(x) ={...,-2,-1,0,1,2,...}?int(x,1)?(-∞,∞)? Open excel and look up the Ceiling function and enter its description below:Open excel and look up the FLOOR function and enter its description below:The greatest integer function returns the greatestinteger less than or equal to the argument.The smallest  integer function returns the smallestinteger greater than the argument. f(x)x0149Domain: xεRange: Equation:a.k.a. f(x)=The inverse of x2 .f(x) ε [0,∞)?f(x) =[0,∞)?SQRT(X)?parent function√x? f(x)x-1-1?-½-⅛?0?0⅛?½1?18?2Equation:Domain: xεRange: parent functiona.k.a. f(x)=The inverse of x3.f(x) =f(x) ε (-∞,∞)?(-∞,∞)?x1/3?∛x? Copy the key press sequence to graph f(x)=∛x. f(x)x-⅓?-3-½?-2-1?-1d.n.e.?01?1½?2⅓?3Equation:Domain: Range:  a.k.a. f(x) =The inverse of x.d.n.e =  parent functiondoes not exist.?{xε ℛ, x≠1}?f(x) ={y∊ℛ, y≠0}?x-1?1/x? ◌ Parent Functions● Piecewise Functions◌ Transforming functions Enter these equationsto graph the peicewisefunction of 4 peices. Press GRAPH.Type codegiven to youby yourteacher. The cieling function rounds up tothe nearest integer away from zero.?CIELING(x,1) =↱x↰The floor function rounds down tothe nearest integer toward zero.?f(x) = int(x) =FLOOR(x,1) =↳x↲{ceiling(x)=↱x↰?floor(x) =↳x↲?x≥0x<0 ◌ Parent Functions◌ Piecewise Functions● Transforming functions Write the transformations made to f(x) to obtain g(x).translation, shift, to the right by      units.reflection over the x-axis indicated bytranslation, shift, up by        units.vertical dilation by a factor of6?2?7?" - "? Write the transformations made to f(x) to obtain g(x).translation to the left by      units.reflection over the x-axis indicated bytranslation down by        units.vertical dilation by a factor of9?7?2?" - "?
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