Use the graph of y = f ( x ) to solve this exercise. a. What are the zeros of f ? b. Find the value(s) of x for which f ( x ) = -1. c. Find the value(s) of x for which f ( x ) = -2. d. Is f even, odd, or neither? e. Does f have an inverse function? f. Is f (0) a relative maximum , a relative minimum, or neither? g. Graph g ( x ) = f ( x + 1 ) − 1. h. Graph h ( x ) = 1 2 f ( 1 2 x ) . . i. Graph r ( x ) = − f ( − x ) + 1. j. Find the average rate of change of f from x 1 = − 2 t o x 2 = 1.
Use the graph of y = f ( x ) to solve this exercise. a. What are the zeros of f ? b. Find the value(s) of x for which f ( x ) = -1. c. Find the value(s) of x for which f ( x ) = -2. d. Is f even, odd, or neither? e. Does f have an inverse function? f. Is f (0) a relative maximum , a relative minimum, or neither? g. Graph g ( x ) = f ( x + 1 ) − 1. h. Graph h ( x ) = 1 2 f ( 1 2 x ) . . i. Graph r ( x ) = − f ( − x ) + 1. j. Find the average rate of change of f from x 1 = − 2 t o x 2 = 1.
Solution Summary: The author explains that the zero of a function is where the graph of function crosses the x -axis.
f. Is f(0) a relative maximum, a relative minimum, or neither?
g. Graph
g
(
x
)
=
f
(
x
+
1
)
−
1.
h. Graph
h
(
x
)
=
1
2
f
(
1
2
x
)
.
.
i. Graph
r
(
x
)
=
−
f
(
−
x
)
+
1.
j. Find the average rate of change of f from
x
1
=
−
2
t
o
x
2
=
1.
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 .
The Course Name Real Analysis please Solve questions by Real Analysis
part 3 of the question is:
A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes.
What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model.
Will the last passenger to board the ride need to wait in order to exit the ride? Explain.
2. The duration of the ride is 15 min.
(a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris
wheel?
(b) What is the position of that passenger when the ride ends?
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