11-1 Square Root Functions - Math Slide Show

Lesson 11-1Objective - To simplify rational and irrationalsquare roots.RealsRationals0 = 01 = 14 = 29 = 316 = 425 = 5Irrationals235678≈1.414≈1.732≈ 2.236≈ 2.449For all real values of n, n ≥ 0.≈ 2.646≈ 2.828Recognizing Rational RootsRational Roots Perfect Squares?0 = 001 = 114 = 249 = 3916 = 41625 = 52536 = 63649 = 74964 = 864Identify each root as rational or irrational.1)2)3)4) −5)1649182025rationalrationalirrationalrationalirrational6)7)8)9) −10)05712199−4rationalirrationalrationalirrationalNeither (not aReal number)Between what two whole numbers does theirrational root lie?1) 10 3) 1049 < 10 < 163< 10 < 42) 20 4) 5716 < 20 < 254 < 20 < 5100 < 104 < 12110 < 104 < 1149 < 57 < 647 < 57 < 8Evaluate. Round to the nearest hundredth whennecessary.1) 121 = 11 4) ± 81 = ± 92) −400= − 205) ± 189 or − 9≈ ± 4.24Evaluate when a = 2, b = 3, and c = -2. Round tonearest hundredth when necessary.21) b − 4ac2)( )( − )23 − 4 2 29+ 16 = 25 = 5b2− 4ac2a( )( −)( )23 −4 2 2223)71≈ 8.436)2±9911.95 or −7.95≈ 2 +9.95or 2−9.959 + 16=254 4=54Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 11-1 (cont.)Evaluate when a = -5, b = 2, and c = -1. Round tonearest hundredth when necessary.23) b − 4ac4)( )( )22 −4 −5 −1a−2cb2 2( −5) − 22 24− 20= −162 ( −1)No Real Root25 − 4−25−2−2=−32Evaluate when a = 2, b = 3, and c = -2. Round tonearest hundredth when necessary.25) − b ± b −4ac6)( )( )− ± − −23 3 4 2 2− 3 ±25−3 ± 5−3 + 5 −3− 52 or −8− ± −2a2b b 4ac( )( )− ± − −2(2)23 3 4 2 2− 3±254− 3±54− 3 + 5=14 2−3−5 = −24Domains for Real RootsState the domain for x in each root below.1) x{x:x∈ Reals, x ≥ 0}2) x + 4{x:x∈ Reals, x ≥−4}3) x − 5{x:x∈ Reals, x ≥ 5}x + 4 ≥0−4 −4x ≥−4x−5≥0+ 5 + 5x ≥ 5Domains for Real RootsState the domain for x in each root below.4) 2x 2x ≥ 02 2{x:x∈ Reals, x ≥ 0}x ≥ 05) 5x −15x −1≥0+ 1 + 1{x:x∈ Reals, x ≥1}5x ≥ 15 5 5x ≥15State the domain of the given functions.6) y =38) y =5xx − 3Domain: x > 0 Domain: x ≥ 0, x≠97)5x2(x + 4)y =9) y =x − 4(x − 3)(2x + 5)Domain: x∈Reals, Domain: x∈Reals,x ≠ 4x ≠ 3,x ≠−52Graphs of Square Root FunctionsGraph. State the domain and range.y = xy6x y50 0 = 041 1 = 132 2 ≈1.423 3 ≈1.714 4 = 25 5 ≈ 2.2 0 1 2 3 4 5 6x6 6 ≈ 2.4 Domain: x ≥ 0 Range: y ≥ 0Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010

Lesson 11-1 (cont.)Graph. State the domain and range.y = 2 x + 1x yy60 2 0 + 1 = 1152 1+ 1= 3242 2 + 1≈ 3.8332 3 + 1≈ 4.5422 4 + 1= 5512 5 + 1≈ 5.56 2 6 + 1≈ 5.9 0 1 2 3 4 5 6xDomain: x ≥ 0 Range: y ≥ 1State the domain and range of the given functions.1) y = x + 1 3) y = 2 x −1Domain:Range:x ≥ 0y≥1Domain:Range:x ≥ 1y≥02) y = x + 3 4) y = 3 x + 4 −2Domain:Range:x ≥−3y≥0Domain:Range:x ≥−4y≥−2Algebra Slide Show: Teaching Made Easy As Pi, by James Wenk © 2010