4.1B Exponential Functions
Objectives:
F.IF.73: Graph exponential and logarithmic functions, showing intercepts and end behavior,
and trigonometric functions, showing period , midline, and amplitude.
F.IF.5: Relate the domain of a function to its graph and , where applicable, to the quantitative
relationship it describes.
A.SSE.1: Interpret expressions that represent a quantity in terms of its context.
For the board: You will be able to write and evaluate exponential expressions to model growth and
decay situations.
Anticipatory Set:
If the parent function f(x) = bx is multiplied by a number, this will create a stretch or compression.
A function of the form f(x) = abx, with a > 0 and b > 1, is an exponential growth function, which
increases as x increases.
Examples: f(x) = 3(5)x
g(x) = ½(7)x
A function of the form f(x) = abx, with a > 0 and 0 < b < 1 is an exponential decay function, which
decreases as x increases.
Examples: f(x) = 8(0.25)x
g(x) = ¾(1/3)x
Open the book to page 235 and read example 1.
Example: Tell whether the function shows growth or decay. Then graph.
These functions are vertical stretches and shrinks of the parent function.
To graph these functions we will use the old fashioned method of setting up a table,
choosing values for x and finding the f(x).
These functions will have a horizontal asymptote at y = 0.
1. f(x) = 10(0.75)x
2. g(x) = 10(1.05)x
0 < b < 1 so decay (a > 0)
x
y
0
10
4
3.2
8
1
12
0.3
b > 1 so growth (a > 0)
16
0.1
x
y
0
10
4
12.1
16
24
12
18
8
12
4
6
0
4
8
12
16
0
4
8
14.8
8
12
18
12
16
21.8
16
Graphing Activity:
Practice: Tell whether the function p(x) = 5(1.2)x shows growth or decay. Then graph.
b > 1 so growth
x -4 -2 -1 0 1 2
4
y 2.4 3.5 4.2 5 6 7.2 10.3
16
12
8
4
-4
-2
0
2
4
Open the book to page 282 and read example 2.
Example: Given g(x) = 2/3 (1.5x), describe the transformations from the parent function, find the yintercept and the asymptote.
Hint: to find the y-intercept, let x = 0 and solve for y.
The function is vertically compressed by a factor of 2/3.
y-intercept: 2/3
asymptote: y = 0
White Board Activity:
Practice: Given each of the following functions, describe the transformations from the parent
function, find the y-intercept and the asymptote.
a. h(x) = 1/3(5x)
The function is vertically compressed by a factor of 1/3.
y-intercept: 1/3
The asymptote is unchanged: y = 0
b. g(x) = 2(2-x)
The function is reflected over the y-axis, then vertically stretched by 2.
y-intercept: 2
The asymptote is unchanged: y = 0
Assessment:
Question student pairs.
Independent Practice:
Text: pgs. 237 – 238 prob. 2 – 4, 7 – 9, 18, 19.
For a Grade:
Text: pgs. 237 – 238 prob. 2, 4. State the asymptote, the domain, and the range.