In Exercises 1-5, graph f and g in the same rectangular coordinate system . Graph and give equations of all asymptotes. Give each function’s domain and range. f ( x ) = 2 x and g ( x ) = 2 x − 3
In Exercises 1-5, graph f and g in the same rectangular coordinate system . Graph and give equations of all asymptotes. Give each function’s domain and range. f ( x ) = 2 x and g ( x ) = 2 x − 3
In Exercises 1-5, graph f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. Give each function’s domain and range.
f
(
x
)
=
2
x
and
g
(
x
)
=
2
x
−
3
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.
Expert Solution
To determine
To calculate: Domain, range and equation of asymptotes for given functions f(x)=2x,g(x)=2x−3.
Answer to Problem 1MCCP
Solution:
Asymptote of f:y=3_.
Asymptote of g:y=−3_.
Domain of f= Domain of g=(−∞,∞).
Range of f=(0,∞)_, Range of g=(−3,∞)_.
Explanation of Solution
Given: The given functions: f(x)=2x,g(x)=2x−3
Calculation:
Create a table of co-ordinates for the given function f(x)=2x
x
-2
-1
0
1
2
f(x)=2x
f(−2)=2−2=122=14
f(−1)=2−1=121=12
f(0)=20=1
f(1)=21=2
f(2)=22=4
Plot these points, connecting them with a curve for graph of f(x)=2x.
To plot the graph of a given function g(x)=bx−c=2x−3, shift the graph of f(x)=bx=2x downwards c=3 units.
Expert Solution
To determine
To graph:f(x)=2x,g(x)=2x−3
Explanation of Solution
Given: The given functions: f(x)=2x,g(x)=2x−3
Graph:
Interpretation:
The graph for f(x)=2x never touches negative portion of x-axis. Hence x-axis or y=0 is asymptote.
The asymptote for g(x)=2x−3 is y=−3.
Domain of f(x)=bxandg(x)=bx−c consists of all real numbers (−∞,∞).
Hence domain of f(x)=2x= domain of g(x)=2x−3=(−∞,∞).
Range of f(x)=bx consists of all positive real numbers (0,∞).
Hence range of f(x)=2x is (0,∞).
From the graph, range of g(x)=2x−3 is (−3,∞).
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