More on Linear Function

8/3/2019 More on Linear Function

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INTRODUCTIONWind Power


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The movement of the atmosphere is driven by differences of temperatur

the Earth's surface due to varying temperatures of the Earth's surface whe

by sunlight. Wind energy can be used to pump water or generate electric

but requires extensive areal coverage to produce significant amounts o

energy.

INTRODUCTION


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GRAPH OF = + More on Linear Functions


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When the slope is positive, or m

the line slants upward to the rig

indicating an increasing linear

function.

GRAPH OF = +

m > 0 (0, b)


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When the slope is negative, or m

the line slants downward to the r

indicating an decreasing linea

function.

GRAPH OF = +

m < 0 (0, b)


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When the slope is zero, or m = 0line is horizontal or parallel to thaxis. The equation of the functi

reduces to the form

=

This is called the constant functEvery value of x corresponds t

constant value of y.

GRAPH OF = +

m = 0

(0, b)


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When the slope is 1, m = 1, and thintercept is zero the line passes

through the origin (0, 0) and slanupward from the third quadrant to

first quadrant dividing the two

quadrants. The equation of thefunction reduces to the form.

= x

This is called the identity functio

GRAPH OF = +

m = 1


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THE ZERO OF THE LINEAR

FUNCTIONMore on Linear Functions


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The Zero of the Linear Function is

the value of the variable x when

is zero.

The zero of the linear function = + is the point where

the line crosses the x-axis.

Example

Find the zero of the linear funct = 2 4

Solution (equate the function to 2 4 = 0

2 = 4

= 2

The zero of the linear = 2

4 is 2

THE ZERO OF THE LINEAR

FUNCTION


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EXAMPLES AND SOLUTIONMore on Linear Functions


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For each linear function, determine (a) the slope and y-intercept, (b) f(-2)

f(2), and (c) the zero of the function

1. f(x) = 3x + 5

2. f(x) = 2x - 1

EXAMPLES


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f(x) = 3x + 5

a. Slope and y-intercept

Slope: 3

y-intercept: 5

b. Function of the followingf(-2) = 3(-2) +5

=-1

f(2) = 3(2) + 5

=11

c. Zero of the function

f(x) = 3x + 5

3x + 5 = 0

3x = -53

3 =

5

3

x =

zero of the function is

or

5

3

, 0

SOLUTION


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f(x) = 2x - 1

a. Slope and y-intercept

Slope: 2

y-intercept: -1

b. Function of the followingf(-2) = 2(-2) - 1

=-5

f(2) = 2(2) - 1

=3

c. Zero of the function

f(x) = 2x - 1

2x 1 = 0

2x = 12

2 =

1

2

x =

zero of the function is

or

1

2, 0

SOLUTION


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EXERCISEMore on Linear Functions


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For each linear function, determine (a) the slope and y-intercept, (b) f(-2) and and (c) the zero of the function

1. f(x) = 4 - x

2. f(x) = 2x3. F(x) = 6x +12

Compute the zero of each linear function

1. F(x) = 5x 1

2. F(x) = 2x + 12

EXERCISE

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