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Core Connections Integrated I, 2013

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Core Connections Integrated I, 2013 View details

1. Section 11.1

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Exercise 20 Page 593

a The expression

f (x) - 2

tells us to subtract

2

from the output of

f (x) .

This results in a vertical translation of

2

in the negative direction. By substituting the expression for

f (x)

we can find the new expression.

f (x) - 2

$f (x) = 8 (x - 3) + 4$

(8 (x - 3) + 4) - 2

Remove parentheses

8 (x - 3) + 4 - 2

Distribute $8$

8 x - 24 + 4 - 2

Add and subtract terms

8 x - 22

b The expression

f (x) - 0.5

tells us to subtract

0.5

from the output of

f (x) .

This results in a vertical translation of

0.5

in the negative direction. By substituting the expression for

f (x)

we can find the new expression.

f (x) - 0.5

$f (x) = 8 (x - 3) + 4$

(8 (x - 3) + 4) - 0.5

Remove parentheses

8 (x - 3) + 4 - 0.5

Distribute $8$

8 x - 24 + 4 - 0.5

Add and subtract terms

8 x - 20.5

c The expression

f (x) + 8

tells us to add

8

to the output of

f (x) .

This results in a vertical translation of

8

in the positive direction. By substituting the expression for

f (x)

we can find the new expression.

f (x) + 8

$f (x) = 8 (x - 3) + 4$

(8 (x - 3) + 4) + 8

Remove parentheses

8 (x - 3) + 4 + 8

Distribute $8$

8 x - 24 + 4 + 8

Add and subtract terms

8 x - 12

d The expression

f (x) + \frac{3}{4}

tells us to add

\frac{3}{4}

to the output of

f (x) .

This results in a vertical translation of

\frac{3}{4}

in the positive direction. By substituting the expression for

f (x)

we can find the new expression.

f (x) + \frac{3}{4}

$f (x) = 8 (x - 3) + 4$

(8 (x - 3) + 4) + \frac{3}{4}

Remove parentheses

8 (x - 3) + 4 + \frac{3}{4}

Distribute $8$

8 x - 24 + 4 + \frac{3}{4}

▼

Simplify

Add terms

8 x - 20 + \frac{3}{4}

$a = \frac{4 \cdot a}{4}$

8 x - \frac{8 0}{4} + \frac{3}{4}

CommutativePropAdd

Commutative Property of Addition

8 x + \frac{3}{4} - \frac{8 0}{4}

Subtract fractions

8 x + \frac{- 7 7}{4}

MoveNegNumToFrac

Put minus sign in front of fraction

8 x + (- \frac{7 7}{4})

Distribute $- 1$

8 x - \frac{7 7}{4}

Subchapter links

11.1.1 Introduction to Constructions p.587-589

11.1.2 Constructing Bisectors p.592-593

11.1.3 More Explorations with Constructions p.597-599