Graphing Exponential Functions Section 4.3. Lehmann, Intermediate Algebra, 4ed Section 4.3 Graph by...

Graphing Exponential Functions

Section 4.3

Lehmann, Intermediate Algebra, 4edSection 4.3

Graph by hand.

Slide 2

Graphing Exponential Functions with b > 1Graphing Exponential Functions

Example 2xf x

Solution• List input–output pairs

(see table)• Input increases by 1 and

output multiplies by 2• Plot these points (see next

slide)

Lehmann, Intermediate Algebra, 4edSection 4.3 Slide 3

Graphing Exponential Functions with b > 1Graphing Exponential Functions

• Use graphing calculator to verify

Solution Continued


Graph by hand.

Slide 4

Graphing Exponential Functions with 0< b < 1Graphing Exponential Functions

Example

14

2

x

g x

Solution• List input–output pairs (see table)

• For example

• (–1, 8) is a solution • x increases by 1, y is multiplied by ½

Lehmann, Intermediate Algebra, 4edSection 4.3 Slide 5

Graphing Exponential Functions with 0< b < 1Graphing Exponential Functions

Solution Continued


For an exponential function of the form y = abx, if the value of the independent variable increases by 1, the value of the dependent variable is multiplied by b.

•For the function , as the value of x increases by 1, the value of y is multiplied by 3

•For the function , as the value of x

increases by 1, the value of y is multiplied by 3/4 Slide 6

Base Multiplier Property; Increase or Decreasing PropertyBase Multiplier Property

Property

Illustration 2 3 xf x

35

4

x

f x


Let , where a > 0. Then•If b > 1, then the function f is increasing. We say that the function grows exponentially (left). •If 0 < b < 1, then the function f is decreasing. We say that the function decays exponentially (right).

Slide 7

Increase or Decrease PropertyBase Multiplier Property

Property xf x a b


For an exponential function of the form

the y-intercept is (0, a).

• The function , the y-intercept is (0, 5)

• The function , the y-intercept is (0, 4)

Slide 8

Y-intercept of an Exponential FunctionIntercepts

Property

xy a b

Illustration 5 8 xf x

14

7

x

f x


Exponential function of the form , the y-intercept is not (0, b). By writing , we see that the y-intercept is (0, 1).

For example, for , the y-intercept is (0, 1).

Let

1. Find the y-intercept of f.

Slide 9

Intercepts and Graph of an Exponential FunctionIntercepts

Warning xy b

Example

1x xy b b

2xy

16

2

x

f x


• is of the form ,

• We know that the y-intercept is (0, a), or (0, 6).

2. Find the x-intercept of f.

• By base multiplier property, x increases by 1, y value multiplies by ½

Slide 10


Solution

16

2

x

f x

xf x a b

Example

Solution


• No number of halvings will result in zero• As x grows large, y gets

closer to the x-axis• Called horizontal

asymptote

3. Graph f by hand.

Slide 11


Example

Solution Continued


• Plot solutions from the table

Slide 12


Solution

• Verify on graphing calculator

Lehmann, Intermediate Algebra, 4ed

The graph of an exponential function f is shown.

1.Find f(2).

•Blue arrow shows input of x = 2 leads to an output y = 8 •f(2) = 8

Section 4.3 Slide 13

Finding Values of a Function from Its GraphReflection Property

Example

Solution


2. Find x when f(x) = 2.

• Red arrow shows output of y = –2 leads to an input x = 2

• x = –2 when f(x) = 2



Example

Solution


3. Find x when f(x) = 0.

• Graphs of exponential functions get close to zero, but never reaches x-axis

• No value of x where f(x) = 0



Example

Solution

Graphing Exponential Functions Section 4.3. Lehmann, Intermediate Algebra, 4ed Section 4.3 Graph by...

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