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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Solve questions by Course Name (Ordinary Differential Equations II 2)
please Solve questions by Course Name( Ordinary Differential Equations II 2)
InThe Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth.
Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth
from which the flash is visible? (Earth’s radius is approximately 4000 miles.)
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