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 .
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Determine if the values of the variables listed are solutions of the system of equations.
2x - y = 4
3x+5y= - 6
x=1, y = 2; (1,-2)
Is (1, 2) a solution of the system of equations?
L
No
Yes
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10. A sound wave's amplitude can be modeled by the function y = −7 sin ((x-1) + 4). Within the interval 0 < x < 12, when does the function have an amplitude
of 4? (Select all that apply.)
9.522 seconds
4.199 seconds
0.522 seconds
1.199 seconds
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