a. Graph f ( x ) = x − 2 . b. From the graph of f , is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Write an equation for f − 1 ( x ) . f. Explain why the restriction x ≥ 0 is placed on f − 1 . g. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system . h. Write the domain of f − 1 in interval notation. i. Write the range of f − 1 in interval notation.
a. Graph f ( x ) = x − 2 . b. From the graph of f , is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Write an equation for f − 1 ( x ) . f. Explain why the restriction x ≥ 0 is placed on f − 1 . g. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system . h. Write the domain of f − 1 in interval notation. i. Write the range of f − 1 in interval notation.
Solution Summary: The author explains how to graph the function f(x)=sqrtx-2.
b. From the graph of f, is f a one-to-one function?
c. Write the domain of f in interval notation.
d. Write the range of f in interval notation.
e. Write an equation for
f
−
1
(
x
)
.
f. Explain why the restriction
x
≥
0
is placed on
f
−
1
.
g. Graph
y
=
f
(
x
)
and
y
=
f
−
1
(
x
)
on the same coordinate system.
h. Write the domain of
f
−
1
in interval notation.
i. Write the range of
f
−
1
in interval notation.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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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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Jamal wants to save $48,000 for a down payment on a home. How much will he need to invest in an
account with 11.8% APR, compounding daily, in order to reach his goal in 10 years? Round to the
nearest dollar.
r
nt
Use the compound interest formula, A (t) = P(1 + 1)".
An account is opened with an intial deposit of $7,500 and earns 3.8% interest compounded semi-
annually. Round all answers to the nearest dollar.
a. What will the account be worth in 10 years? $
b. What if the interest were compounding monthly? $
c. What if the interest were compounded daily (assume 365 days in a year)? $
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