MTH405_Wk_5_Tutorial

# MTH405_Wk_5_Tutorial - MTH405 Wk 5 Tutorial Linear Graphs...

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Unformatted text preview: MTH405 Wk 5 Tutorial Linear Graphs Sketch the following functions. 1. y = 3x + 5. 2. y = −x. 3. y = −x + 2. 4. 2y − 4x − 4 = 0. 5. y = 3, x ∈ R. 6. x = 2, y ∈ R. Quadratic Graphs Sketch the following functions. 1. y = x2 + 3 2. y = (x − 4)2 + 2 3. y = x − x2 4. y = x2 + 5x + 4 5. y = x2 − x − 12. Cubic Graphs Sketch the following functions. 1. y = x3 − 2 2. y = 4x3 − 8x2 − 15x + 9 3. y = 2x3 − 7x2 + 4x + 4 4. y = 4x3 + 4x2 − 11x − 6 5. y = x3 − 2x2 − 5x + 6 1 Rational Graphs Sketch the following functions. 1. y = 3x+4 4x+5 2. y = 3x+4 4x2 +5 3. y = x2 −6 x−2 4. y = x+1 x2 −2 5. y = x2 −5 x+3 When nding horizontal asymptote in rational functions, check if function is balanced, top heavy or bottom heavy. For Remark. • balanced rational function - HA=DIVISION OF THE COEFFICIENTS OF THE TERMS WITH THE HIGHEST POWER. • bottom heavy - HA = 0 a = 0. • top heavy - OA=DIVISION OF THE RATIONAL PROPERLY TO MAKE IT BOTTOM HEAVY, SO WE GET A PROPER FRACTION (TERM PLUS A FRACTION). Example: x2 − 6 −2 = (x + 2) + . x−2 x−2 The the Oblique Asymptote is x + 2. Trigonometric Graphs Exercise. Sketch the following functions. 1. y = 2 sin x 2. y = − cos x 3. y = sin x + 1 4. y = sin(x + 30◦ ) 5. y = 2 cos(x − 60◦ ) 6. y = sin 2x 7. y = 3 sin 2x 8. y = 3 cos(4x − 90◦ ). 2 Additional Questions (Simultaneous Equations, Finding Roots, Quadratic formula) Solve the following simultaneous equations and verify the results. 1. a + b = 7 , a − b = 3 2. 2x + 5y = 7 , x + 3y = 4 3. 3s + 2t = 12 , 4s − t = 5 4. 3x − 2y = 13 , 2x + 5y = −4 Solve for x. 1. 3x − 2 = x + 4 2. 2(x + 6) − (x − 2) = 3(8 − x) 3. 3 x 4. 2x 3 + 5 x + =2 2x 5 = 1.6 5. x2 − x − 4 = 2 6. 3x2 − 12x = 0 7. x2 − 6x + 9 = 0 8. 2x2 − 5x − 4 = 0 3 ...
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