The Chemistry Maths Book, Second Edition

58 Chapter 2Algebraic functions

This has rootsx

1

1 = 1 − 4 andx

2

1 = 14 , with corresponding value of y,y

1

1 = 14 andy

2

1 = 1 − 2.

In this case the two solutions are the points at which the straight line crosses the

ellipse;(x

1

, y

1

) 1 = 1 (−4, 4)and(x

2

, y

2

) 1 = 1 (4, −2), as in Figure 2.15.

0 Exercises 71–73

2.9 Exercises

Section 2.1

1.Find the values ofy 1 = 121 − 13 xfor:

(i)x 1 = 10 (ii)x 1 = 12 (iii)x 1 = 1 − 3 (iv)x 1 = 1223

2.Find the values ofy 1 = 12 x

2

1 + 13 x 1 − 11 for:

(i)x 1 = 10 (ii)x 1 = 11 (iii)x 1 = 1 − 1 (iv)x 1 = 1 − 223

3.Givenf(x) 1 = 1 x

3

1 − 13 x

2

1 + 14 x 1 − 13 , find:

(i)f(5) (ii)f(0) (iii)f(−2) (iv)f(− 22 3)

4.Iff(x) 1 = 12 x

2

1 + 14 x 1 + 13 , what is:

(i)f(a) (ii)f(y

2

)

5.Iff(x) 1 = 1 x

2

1 − 13 x 1 − 14 , what is:

(i)f(a 1 + 1 3) (ii)f(a

2

1 + 1 1) (iii)f(x 1 + 1 1) (iv)f(x

2

1 − 13 x 1 − 1 4)

6.Iff(x) 1 = 12 x 1 − 11 andg(x) 1 = 13 x 1 + 11 , expressf(g)as a function of x.

Section 2.2

Make a table of (x, y) values and sketch a fully labelled graph of the quadratic:

7.y 1 = 1 x

2

1 − 14 x 8.y 1 = 1 −x

2

1 − 1 x 1 + 12

Section 2.3

Factorize:

6 x

2

y

2

1 − 12 xy

3

1 − 14 y

2

10.x

2

1 + 16 x 1 + 15 11.x

2

1 + 1 x 1 − 16

12.x

2

1 − 18 x 1 + 115 13.x

2

1 − 14 14. 4 x

2

1 − 19

2 x

2

1 + 1 x 1 − 16 16.x

4

1 − 110 x

2

1 + 19

x

y

4

− 2

− 4

4

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Figure 2.15