Honors Algebra 2 (5th Hour, Fall 2011): Notes from 9-8-11

Sunday, September 11, 2011

Notes from 9-8-11

Section 1.2

Absolute Value Practice

1) 3-2 |4-x| = -11

-2 |4-x| = -14

|4-x| = 7

4-x = 7 -4+x = 7

x = -3 x = 11

2) |2x-3| < 9

2x-3 < 9 -2x+3 < 9

2x < 12 -2x < 6

x < 6 x > -3

-3 < x < 6

Interval Notation:

-3 $<$ x $<$ 6 can also be expressed as (-3, 6)

-3 $\leq$ x $\leq$ 6 can also be expressed as [-3, 6]

3) |x+3| + |2-5x| = 7

Critical Values: when the expression inside of the absolute value turns to zero

critical value of |x+3| = -3

critical value of |2-5x| = 2/5

If x < -3:

$- (x + 3) +2 -5x = 7$

$-x - 3 + 2 -5x = 7$

$-6x -1 = 7$

$-6x = 8$

$x = -\frac{4}{3}$

x is not less than -3

If -3 < x < 2/5:

$x + 3 + 2 - 5x + 7$

$-4x + 5 = 7$

$-4x = 2$

$x = -\frac{1}{2}$

√

If x > 2/5:

$-(2-5x) + x + 3 = 7$

$-2 + 5x + x + 3 = 7$

$6x + 1 = 7$

$6x = 6$

$x = 1$

√

Exponents

$5\cdot 5\cdot 5\cdot 5\cdot 5 = 5^{6}$

$x^{m}$ · $x^{n}$ = $x^{m+n}$

$ex: x^{3}\cdot x^{2} = (x\cdot x\cdot x) \cdot (x\cdot x) = x^{3+2} = x^{5}$

$\frac{x^{m}}{x^{n}} = x^{m-n}$

$ex :\frac{5^{4}}{5^{2}} = \frac{5\cdot 5\cdot 5\cdot 5}{5\cdot 5} = 5^{4-2} = 5^{2}$

$x^{-n} = \frac{1}{x^{n}}$

$ex: \frac{5^{4}}{5^{6}} = \frac{1}{5^{2}} = 5^{-2}$

$\frac{1}{x^{-2}} = x^{2}$

$(x^{m})^{n} = x^{m\cdot n}$

$ex: (2^{3})^{2} = (2\cdot 2\cdot 2) \cdot (2\cdot 2\cdot 2) = 2^{6}$

Square Roots

$\sqrt{x} = x^{\frac{1}{2}}$ $\sqrt[3]{x} = x^{\frac{1}{3}}$

$x^{\frac{4}{3}} = (x^{\frac{1}{3}})^{4} = \sqrt[3]{x}^{4} or \sqrt[3]{x^{4}}$

-Carly

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