Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x -intercepts d. they y -intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. values of x for which f ( x ) ≤ 0 h. the numbers at which f has a relative maximum i. the relative maxima of f j. f ( − 2 ) k. the values of x for which f ( x ) − 0 i. Is f even, odd, or neither?
Use the graph of f to determine each of the following. Where applicable, use interval notation. a. the domain of f b. the range of f c. the x -intercepts d. they y -intercept e. intervals on which f is increasing f. intervals on which f is decreasing g. values of x for which f ( x ) ≤ 0 h. the numbers at which f has a relative maximum i. the relative maxima of f j. f ( − 2 ) k. the values of x for which f ( x ) − 0 i. Is f even, odd, or neither?
Solution Summary: The author explains that the values that are the input to a function are known as the domain of the function.
Use the graph of f to determine each of the following. Where applicable, use interval notation.
a. the domain of f
b. the range of f
c. the x-intercepts
d. they y-intercept
e. intervals on which f is increasing
f. intervals on which f is decreasing
g. values of x for which
f
(
x
)
≤
0
h. the numbers at which f has a relative maximum
i. the relative maxima of f
j.
f
(
−
2
)
k. the values of x for which
f
(
x
)
−
0
i. Is f even, odd, or neither?
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements. a. No, because more money should have been earned through simple interest than compound interest. b. Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. c. No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal. d. Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.
Compare and contrast the simple and compound interest formulas. Which one of the following statements is correct? a. Simple interest and compound interest formulas both yield principal plus interest, so you must subtract the principal to get the amount of interest. b. Simple interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest; Compound interest formula yields only interest, which you must add to the principal to get the final amount. c. Simple interest formula yields only interest, which you must add to the principal to get the final amount; Compound interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest. d. Simple interest and compound interest formulas both yield only interest, which you must add to the principal to get the final amount.
Sara would like to go on a vacation in 5 years and she expects her total costs to be $3000. If she invests $2500 into a savings account for those 5 years at 8% interest, compounding semi-annually, how much money will she have? Round your answer to the nearest cent. Show you work. Will she be able to go on vacation? Why or why not?
Chapter 2 Solutions
Algebra & Trigonometry With Additional Material From College Algebra Essentials (custom Edition For Tidewater Community College)
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