<< Chapter < Page Chapter >> Page >

Shifts of the parent function f ( x ) = b x

For any constants c and d , the function f ( x ) = b x + c + d shifts the parent function f ( x ) = b x

  • vertically d units, in the same direction of the sign of d .
  • horizontally c units, in the opposite direction of the sign of c .
  • The y -intercept becomes ( 0 , b c + d ) .
  • The horizontal asymptote becomes y = d .
  • The range becomes ( d , ) .
  • The domain, ( , ) , remains unchanged.

Given an exponential function with the form f ( x ) = b x + c + d , graph the translation.

  1. Draw the horizontal asymptote y = d .
  2. Identify the shift as ( c , d ) . Shift the graph of f ( x ) = b x left c units if c is positive, and right c units if c is negative.
  3. Shift the graph of f ( x ) = b x up d units if d is positive, and down d units if d is negative.
  4. State the domain, ( , ) , the range, ( d , ) , and the horizontal asymptote y = d .

Graphing a shift of an exponential function

Graph f ( x ) = 2 x + 1 3. State the domain, range, and asymptote.

We have an exponential equation of the form f ( x ) = b x + c + d , with b = 2 , c = 1 , and d = 3.

Draw the horizontal asymptote y = d , so draw y = −3.

Identify the shift as ( c , d ) , so the shift is ( 1 , −3 ) .

Shift the graph of f ( x ) = b x left 1 units and down 3 units.

Graph of the function, f(x) = 2^(x+1)-3, with an asymptote at y=-3. Labeled points in the graph are (-1, -2), (0, -1), and (1, 1).

The domain is ( , ) ; the range is ( 3 , ) ; the horizontal asymptote is y = −3.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Graph f ( x ) = 2 x 1 + 3. State domain, range, and asymptote.

The domain is ( , ) ; the range is ( 3 , ) ; the horizontal asymptote is y = 3.

Graph of the function, f(x) = 2^(x-1)+3, with an asymptote at y=3. Labeled points in the graph are (-1, 3.25), (0, 3.5), and (1, 4).
Got questions? Get instant answers now!

Given an equation of the form f ( x ) = b x + c + d for x , use a graphing calculator to approximate the solution.

  • Press [Y=] . Enter the given exponential equation in the line headed “ Y 1 = ”.
  • Enter the given value for f ( x ) in the line headed “ Y 2 = ”.
  • Press [WINDOW] . Adjust the y -axis so that it includes the value entered for “ Y 2 = ”.
  • Press [GRAPH] to observe the graph of the exponential function along with the line for the specified value of f ( x ) .
  • To find the value of x , we compute the point of intersection. Press [2ND] then [CALC] . Select “intersect” and press [ENTER] three times. The point of intersection gives the value of x for the indicated value of the function.

Approximating the solution of an exponential equation

Solve 42 = 1.2 ( 5 ) x + 2.8 graphically. Round to the nearest thousandth.

Press [Y=] and enter 1.2 ( 5 ) x + 2.8 next to Y 1 =. Then enter 42 next to Y2= . For a window, use the values –3 to 3 for x and –5 to 55 for y . Press [GRAPH] . The graphs should intersect somewhere near x = 2.

For a better approximation, press [2ND] then [CALC] . Select [5: intersect] and press [ENTER] three times. The x -coordinate of the point of intersection is displayed as 2.1661943. (Your answer may be different if you use a different window or use a different value for Guess? ) To the nearest thousandth, x 2.166.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Solve 4 = 7.85 ( 1.15 ) x 2.27 graphically. Round to the nearest thousandth.

x 1.608

Got questions? Get instant answers now!

Graphing a stretch or compression

While horizontal and vertical shifts involve adding constants to the input or to the function itself, a stretch or compression occurs when we multiply the parent function f ( x ) = b x by a constant | a | > 0. For example, if we begin by graphing the parent function f ( x ) = 2 x , we can then graph the stretch, using a = 3 , to get g ( x ) = 3 ( 2 ) x as shown on the left in [link] , and the compression, using a = 1 3 , to get h ( x ) = 1 3 ( 2 ) x as shown on the right in [link] .

Questions & Answers

Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
how many start and codon
Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Destiny Reply
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask