f(x) = x2 x > 3 Find the range of f(x) f(x) > 9

Find f-1(x) and state its domain f(x) = x2 + 6x + 8 x > 0 Find f-1(x) and state its domain 𝑓 −1 𝑥 = 𝑥+1 −3 Domain x > 8

f(x) = x2 – 3 g(x) = e2x Find gf(x) fg(x) 𝑒 2 𝑥 2 −6 𝑒 4𝑥 −3

Define the transformations f(x) = x2 Define the transformations 𝑓 𝑥 =2− 𝑥 2 𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 0 −2 𝑓𝑜𝑙𝑙𝑜𝑤𝑒𝑑 𝑏𝑦 𝑎 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑥−𝑎𝑥𝑖𝑠 or 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑥−𝑎𝑥𝑖𝑠 𝑓𝑜𝑙𝑙𝑜𝑤𝑒𝑑 𝑏𝑦 𝑎 𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 0 2

Define the transformations f(x) = x2 Define the transformations 𝑓 𝑥 =2 𝑥 2 −4 𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 0 −2 𝑓𝑜𝑙𝑙𝑜𝑤𝑒𝑑 𝑏𝑦 𝑎 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 2 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑡ℎ𝑒 𝑦−𝑎𝑥𝑖𝑠 Or 𝑠𝑡𝑟𝑒𝑡𝑐ℎ 𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 2 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑡ℎ𝑒 𝑦−𝑎𝑥𝑖𝑠 𝑓𝑜𝑙𝑙𝑜𝑤𝑒𝑑 𝑏𝑦 𝑎 𝑡𝑟𝑎𝑛𝑠𝑙𝑎𝑡𝑖𝑜𝑛 0 −4

Differentiate with respect to x 𝑒 𝑥 2 2cos ½x e3x −sin⁡ 𝑥 2 3 𝑒 3𝑥 ⁡ 2𝑥 𝑒 𝑥 2 ⁡

Sketch the graph of y = 2 𝑒 −2𝑥

Sketch the graph of y = 3ln(x+2)

Sketch the graph of y = |ln x−2 |

Sketch the graph of y = |9 – 4x2|

Sketch the graph of y = e|2x|

Differentiate with respect to x − 2𝑥 2− 𝑥 2 ⁡ 2 𝑥 ⁡ 18x(3x2+4)2⁡ (3x2 + 4)3 ln (2- x2) ln (3x2) e5-x − 𝑒 5−𝑥

x2e2x = 2xe2x Solve 𝑥 2 𝑒 2𝑥 𝑥 𝑒 2𝑥 =2 so x = 2 There are two solutions so what is wrong with this method? 𝑥 2 𝑒 2𝑥 𝑥 𝑒 2𝑥 =2 so x = 2

Solve x2e2x = 2xe2x x2e2x - 2xe2x = 0 xe2x (x – 2)=0 x = 0 x = 2

Sketch the graph of y = sin-1(x)

Sketch the graph of y = cos-1(x-1)

y = 𝑒 3𝑥 ( 𝑥 2 −2) 1 3 Find 𝑑𝑦 𝑑𝑥 2 3 𝑥𝑒 3𝑥 ( 𝑥 2 −2) − 2 3 +3 𝑒 3𝑥 ( 𝑥 2 −2) 1 3

y = 6𝑥−1 𝑠𝑖𝑛2𝑥 Find 𝑑𝑦 𝑑𝑥 6𝑠𝑖𝑛2𝑥−2 6𝑥−1 𝑐𝑜𝑠2𝑥 𝑠𝑖𝑛 2 2𝑥

𝐷𝑜𝑛′𝑡 𝑓𝑜𝑟𝑔𝑒𝑡 +𝑐 2 2𝑥+3 4sin 2x e3x 1 3 𝑒 3𝑥 −2𝑐𝑜𝑠2𝑥 ln⁡|2𝑥+3| Integrate with respect to x 2 2𝑥+3 4sin 2x e3x 1 3 𝑒 3𝑥 −2𝑐𝑜𝑠2𝑥 ln⁡|2𝑥+3| 𝐷𝑜𝑛′𝑡 𝑓𝑜𝑟𝑔𝑒𝑡 +𝑐

𝐷𝑜𝑛′𝑡 𝑓𝑜𝑟𝑔𝑒𝑡 +𝑐 4𝑥 (1+𝑥 2 ) 1 1−2𝑥 4 (1+2𝑥) 2 − 2 1+2𝑥 2ln⁡(1+ 𝑥 2 ) Integrate with respect to x − 2 1+2𝑥 2ln⁡(1+ 𝑥 2 ) − 1 2 ln⁡|1−2𝑥| 4𝑥 (1+𝑥 2 ) 1 1−2𝑥 4 (1+2𝑥) 2 𝐷𝑜𝑛′𝑡 𝑓𝑜𝑟𝑔𝑒𝑡 +𝑐

Don’t forget the final statement y = 3ln(3e – x) intersects the line y = x at x = ∝ . Show that ∝ between 4 and 5 Don’t forget the final statement

STAIRCASE x1 x2 x3

Numerical Integration Simpsons rule 0 𝜋 𝑥𝑠𝑖𝑛2𝑥 𝑑𝑥 with 5 ordinates Is your calculator in radians? If possible work with exact values…. Show values in a table. Write the formula out with your values substituted in

Numerical Integration Mid-ordinate rule 0 𝜋 𝑥𝑠𝑖𝑛2𝑥 𝑑𝑥 with 4 strips What are the x-values you would use ?