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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 Spring '16
 Alveen Chand
 Fraction, Rational function, following functions

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