Eponentil & Power Grphs EXPONENTIAL & POWER GRAPHS www.mthletics.com.u
Eponentil EXPONENTIAL & Power & Grphs POWER GRAPHS These re grphs which result from equtions tht re not liner or qudrtic. The eponentil grph hs the vrile s the eponent. The power grphs rise the vrile to n power n. Answer these questions, efore working through the chpter. I used to think: Which of these equtions is for n eponentil grph nd which is for power grph: = 7 or = 7? For which vlue of is equl to zero? Is it possile for = to e negtive? Wh? Answer these questions, fter working through the chpter. But now I think: Which of these equtions is for n eponentil grph nd which is for power grph: = 7 or = 7? For which vlue of is equl to zero? Is it possile for = to e negtive? Wh? Wht do I know now tht I didn t know efore? 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Bsics Eponentil Grphs Eponentil grphs re of functions with the vrile in the eponent of the form The hve this form: = = ` j = or = ` j where. This could lso e written s - ^,h ^-,h Here re some importnt properties out eponentil grphs: The lws cut the -is t ^0, h since 0 = for n vlue of. The eponentil grph never cuts the -is since is never negtive or zero if 0. The greter the vlue of (the se), the steeper the curve. Sketch the grphs of = nd = ` j on the sme set of es = ` j = ^-, h ^, h ^-, 0. h ^0,. h The -intercept of ALL eponentil curves is lws ^0, h - - 0 No -intercepts K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Bsics The grphs elow re of the functions = nd = 0 9 = = (Steeper (Gentler curve) curve) 8 7 6 - - - - - 0 Which is the steeper curve? = is steeper thn =. This is ecuse. Wht is the -intercept of ech curve? Both curves hve -intercept ^0, h c Wh do oth curves hve the sme -intercept? An eponentil curve = will hve -intercept since 0 =. d Do either of the curves ever touch the -is? No, the curves get ver close to the -is ut never touch. This is ecuse there is no vlue for such tht = or = is negtive or zero. 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Bsics Wht out Negtive Grphs? If there is minus (-) in front of the eponentil (eg. =- or =- - ) then the grph is reflected out the -is. Grphicll it looks like the grph is flipped upside down. Sketch the grph of =- ^, h The grph of =- is drwn flipping the grph of = out the -is. This is like flipping the grph of = upside down. = - - 0 - - =- - ^, -h - The sme is done for =- - - or = ` - j : Sketch the grph of =- - ^-, h The grph of =- - is drwn flipping the grph of = - out the -is. This is like flipping the grph of = - upside down. - - 0 - = - =- - ^-,h - - - K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Bsics. The curve elow represents =. Find the missing vlues in the sketch. ^, d h c d ^, c h ^-, ^-, e h f h ^0, ^, h h e f. Without sketching the grphs, identif the -intercepts of = 6 nd = 0. How do ou know this?. The two curves elow represent = nd = 8. Identif ech grph nd nswer these questions: Identif the coordintes of ech point: A = B = E C = D = D E = F = F B A Wh is A common on oth curves? - - - 0 C 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Questions Bsics. The grph elow represents = ` j. Identif the coordintes of ech point using the eqution: A = B = C C = D = B A - - - 0 D Wht re the intercepts of the eqution = ` j?. The curve elow represents =-. Find: ^-, e h ^0, h ^, h ^, c h c d ^, d h e 6 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Bsics 6. Sketch the grphs of these equtions on the es elow: = = - 6 0 9 8 7 6 - - - -0-9 -8-7 -6 - - - - - 0 6 7 8 9 0 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K 7 SERIES TOPIC
Eponentil & Power Grphs Questions Bsics 7. Sketch the grphs of these equtions on the es elow: = - =- - 0 9 8 7 6-6 - - - - - 0 6 - - - - - -6-7 -8-9 -0 - - - - 8 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Knowing More Sketching Power Grphs Power grphs re drwn from the eqution n = where is constnt nd the eponent n is positive integer. Here re some emples where is positive: = ( =, n = ) = ( =, n = ) - - - - 0 - - - - - 0 - - - - If n =, the grph is stright line - - - If n =, the grph is prols = ( =, n = ) = ( =, n = ) - - - - 0 - - - - 0 - Inflection point - - - - - - - Cn ou see pttern? There is generll pttern when is positive ( 0): If n is odd: As the grph moves from left to right, the grph moves up from negtive, through the origin nd then increses s it moves to the right. If n is even: As the grph moves from left to right, the grph moves down from positive, touches the origin nd then increses s it moves to the right. The greter the vlue of or n, the steeper the curve. The smller the vlue of or n, the gentler the curve. 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K 9 SERIES TOPIC
Eponentil & Power Grphs Knowing More Sketching Power Grphs when is Negtive Grphs drwn from = n where is negtive ( 0) ehve in the opposite w. Here re some emples where is negtive: =- ( =-, n = ) =- ( =-, n = ) - - - - 0 - - - - - 0 - - - - - - - =- ( =-, n = ) =- ( =-, n = ) Inflection point - - - - 0 - - - - 0 - - - - - - - - Cn ou see pttern? There is generll pttern when is negtive ( 0): If n is odd: As the grph moves from left to right, the grph moves down from positive, through the origin, nd then decreses s it moves right. If n is even: As the grph moves from left to right, the grph moves up from negtive, touches the origin nd then decreses (moved down) in the negtive direction. The greter the vlue of or n, the steeper the curve. The smller the vlue of or n, the gentler the curve. 0 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Knowing More Here re some emples of how to drw power grphs: Sketch the grphs of these equtions = = (positive) nd n = (even) Step : Plot the points for =-, = 0, =. Step : Drw the grph through these points. Strt here nd move down Move up through here Strt here nd move down Move up through here - - - - 0 - - Pss through the origin - - - - 0 - - Pss through the origin - - - - =- =- (negtive) nd n = (odd) Step : Plot the points for =-, = 0, =. Step : Drw the grph through these points. Strt here nd move down Pss through the origin Move down through here Strt here nd move down Pss through the origin - - - - 0 - - - - 0 - Inflection point - - - - - Move down through here - - 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Questions Knowing More. Eplin the role of nd n in the function n =.. Identif nd n nd then sketch the grphs of these equtions: = = + c = d = - K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Knowing More. Sketch the grphs for these equtions: = 6 = c =- 8 d =- 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Using Our Knowledge Shifting Power Grphs Verticll n n This hppens when the eqution is given s = + d or = - d. n For the cse of = + d, shift the power grph up d units. n For the cse of = - d, shift the power grph down d units. Here re some emples: Drw the grphs for these equtions: = + Step : Drw the grph of =. Step : Shift this grph up units. 8 8 7 7 6 6 units - - - - 0 - - - - 0 =- - Step : Drw the grph of =-. Step : Shift this grph down units. - - - - 0 - - - - 0 - - units - - - - - - - - K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Using Our Knowledge Shifting Eponentil Grphs Verticll This hppens when the eqution is given s = + d or = -d For the cse of = + d, shift the power grph up d units. For the cse of = - d, shift the power grph down d units. Here re some emples: Drw the grphs for these equtions: = - Step : Drw the grph of =. Step : Shift the grph down units. - - - - 0 - - - - - - 0 - units - - - - =- + Imgine -is shifts too Step : Drw the grph of =- -. Step : Shift this grph up units. units - - - - 0 - - - - 0 - - - - - - - - 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Questions Using Our Knowledge. Sketch the power grphs for these equtions: = - =- + 6 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Using Our Knowledge c 6 = + d 7 =- - 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K 7 SERIES TOPIC
Eponentil & Power Grphs Questions Using Our Knowledge. Sketch the eponentil grphs for these equtions: = - = ` j + 8 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Using Our Knowledge c =- + d - =- - 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K 9 SERIES TOPIC
Eponentil & Power Grphs Thinking More Shifting Power Grphs Horizontll Grphs cn lso e shifted sidews. This hppens when the eqution is given s = ^-kh n or = ^+ kh n. For the cse of = ^-kh n, shift the power grph of = n right k units. For the cse of = ^+ kh n, shift the power grph of = n left k units. Here re some emples: Drw the grphs for these equtions = ^-h Plus (-) mens shift right Step : Drw the grph of =. Step : Shift this grph units to the right. 8 7 6 8 7 6 units - - - - 0 - - - - 0 =- ^+ h Plus (+) mens shift left Step : Drw the grph of =-. Step : Shift this grph unit to the left. - - - - 0 - - - - 0 - - - - - - - - - - unit 0 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Thinking More Shifting Eponentil Grphs Horizontll This hppens when the eqution is given s = - k or = + k For the cse of k = -, shift the eponentil grph = to the right k units. For the cse of k = +, shift the eponentil grph = to the left k units. Here re some emples: Drw the grphs for these equtions = + Plus (+) mens shift left Step : Drw the grph of =. Step : Shift this grph up unit to the left. unit - - - - 0 - - - - - 0 - - - - - ^ =- - - h Step : Drw the grph of Minus (-) mens shift right =- -. Step : Shift this grph units to the right. - - 0 6 - - 0 6 - - - - - units - - - 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Questions Thinking More. Sketch the power grphs for these equtions: = ^-h =- ^+ h K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Thinking More. Sketch the eponentil grphs for these equtions: = + = - 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Questions Thinking More. The solid grph elow hs the eqution = : - - - - - 0 - - - - - The dotted curve is verticl trnsformtion of the solid curve. Find the eqution for the dotted curve. Wht is the -intercept of the dotted curve? Is this wht ou epected? c Find the eqution of the dshed line, if it is horizontl trnsformtion of the solid curve. K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Questions Thinking More. The solid grph elow hs the eqution = : c The dshed curve is horizontl trnsformtion of the solid curve. Find the eqution of this curve. The dotted line is verticl trnsformtion of the solid curve. Find the eqution of this curve. Wht is the -intercept of the solid curve? 6 0 9 8 7 6 A - - - 0 d Wht is the -intercept of the dotted curve? Is this wht ou were epecting? e Find the coordintes of the point lelled A. 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Answers Bsics: Bsics:. = = 6. c = d 8 = = - = e = f =. Both grphs hve the -intercept t = s eponentil grphs lws intercept the -is t (0,) since 0 = for n vlue of.. A = ^0, h B =, `- j C =, `- 8 j D = ^, h E = ^8, h F = `, j Eponentil grphs lws intercept the -is t (0, ) since 0 = for n vlue of. 7. = -. A = (0,) B = (-,) C = (-,9) D = (, ) The -intercept is t = nd the grph does not intercept the - is. =- =- c =- d 8 =- e = - =- - 6 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Answers Knowing More: Knowing More:. when is positive ( > 0):. =, n = If n is odd: As the grph moves from left to right, the grph moves up from negtive, through the origin nd then increses s it moves to the right. If n is even: As the grph moves from left to right, the grph moves down from positive, touches the origin nd then increses s it moves to the right. when is negtive ( < 0): c =, n = If n is odd: As the grph moves from left to right, the grph moves down from positive, through the origin nd then decreses s it moves to the right. If n is even: As the grph moves from left to right, the grph moves up from negtive, touches the origin nd then decreses in the negtive direction. The greter the vlue of or n, the steeper the curve. The smller the vlue of or n, the gentler the curve. d =, n =. =, n =. = 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K 7 SERIES TOPIC
Eponentil & Power Grphs Answers Knowing More:. = 6. Using Our Knowledge: = - c =- 8 =- + d =- c = + 6 7 d =- - 8 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Answers Using Our Knowledge: Using Our Knowledge:. = -. d - =- - = ` j + Thinking More:. = ^-h c =- + =- ^+ h 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K 9 SERIES TOPIC
Eponentil & Power Grphs Answers Thinking More:. = + = -. c = - The -intercept is t =-. This is epected s it is units down from the -intercept of = = ( -). c d e ( ) = + = + The -intercept of the solid curve is = The -intercept of the dotted curve is = The coordintes of A re (-, ) 0 K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning
Eponentil & Power Grphs Notes 00% Eponentil nd Power Grphs Mthletics 00% P Lerning K SERIES TOPIC
Eponentil & Power Grphs Notes K 00% Eponentil nd Power Grphs SERIES TOPIC Mthletics 00% P Lerning