Sketching Transformations of Monomial Functions In Exercises 15-18, sketch the graph of y = x n and each transformation. y = x 3 a f ( x ) = ( x + 3 ) 4 b f ( x ) = x 4 – 3 c f ( x ) = 4 – x 4 d f ( x ) = 1 2 ( x – 1 ) 4 e f ( x ) = ( 2 x ) 4 + 1 f f ( x ) = 1 2 x 4 – 2
Sketching Transformations of Monomial Functions In Exercises 15-18, sketch the graph of y = x n and each transformation. y = x 3 a f ( x ) = ( x + 3 ) 4 b f ( x ) = x 4 – 3 c f ( x ) = 4 – x 4 d f ( x ) = 1 2 ( x – 1 ) 4 e f ( x ) = ( 2 x ) 4 + 1 f f ( x ) = 1 2 x 4 – 2
Solution Summary: The author explains how to sketch the graph of the function y=x4 and its transformation.
In 2010, an investor put money into a fund. The graph below shows the value v = v(d) of the investment, in dollars, as a function of the date d.
v(d) Investment value
$305,000
$255,000-
$205,000+
$155,000+
$105,000
$55,000-
$5,000
2010 2020 2030 2040 2050 2060
d = Date
Express the original investment using functional notation.
2010
)
Give the value of the above term.
$
(b) Is the graph concave up or concave down?
concave up
concave down
Explain what this means about the growth in value of the account.
This means that the investment is increasing
(c) In what year will the value of the investment reach $105,000?
2050
(d) What is the average yearly increase from 2050 to 2060?
$
per year
at an increasing ✓
Explain your reasoning.
(e) Which is larger, the average yearly increase from 2050 to 2060 or the average yearly increase from 2010 to 2020?
2010 to 2020
2050 to 2060
The average yearly increase from 2010 to 2020 is $
rate.
C. The average yearly increase from 2050 to 2060 is $
Use the graph to evaluate each expression.
(a) (f+g)(-2)
(b) (f - g)(1)
(c) (fg)(0)
(d) (1)
(a) (f+g)(-2) =
Z
4-
24
4-
[y=f(x)
-y-g(x)
►
O
N
A function, f(x), has a domain of D:{x|x >_-2} and a range of R:{y|y<_-3}. Determine the domain and range of the function after the following transformations were applied: -2f(x-5)+3.
Chapter 3 Solutions
Bundle: College Algebra, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's College Algebra, 10th Edition, Single-Term
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