Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    1
    ReputationRep:
    Simple question: How do you transform the graph f(x) = e^x to f(x) = e^kx?
    I thought you had to stretch it by factor e^k in the x-direction but it's actually by factor 1/k. Don't understand why this is :confused:
    Offline

    16
    ReputationRep:
    You're making the independent variable increase k times as fast, so you squish it. You can check it for x=1, the old f(x) will be e, the new will be e^k, so for k>1 it will have shot up faster, for k<1 it will be a slower increase.
    Offline

    1
    ReputationRep:
    For a function f(x), f(kx) will stretch it parallel to the x-axis with scale factor 1/k.

    If you can't remember the transformations, try considering the graphs of  y = x^2 (for translations and reflections) and  y = sinx for stretches. Works for me.

    (You seem to have got negged for no reason, so here's a free rep back )
    Offline

    5
    ReputationRep:
    (Original post by gildartz)
    Simple question: How do you transform the graph f(x) = e^x to f(x) = e^kx?
    I thought you had to stretch it by factor e^k in the x-direction but it's actually by factor 1/k. Don't understand why this is :confused:
    The reason is that for every x value in the new function, the value of kx is k times larger than the value of x in f(x)=e^x. This means that the new x inputs need to be k times smaller to produce the same outputs as before.

    x \times  k \times  \frac{1}{k} = x

    This results in a stretch of scale factor 1/k parallel to the x axis.
    • Thread Starter
    Offline

    1
    ReputationRep:
    Ah I see, thanks for the help everyone

    (Original post by Goldfishy)
    For a function f(x), f(kx) will stretch it parallel to the x-axis with scale factor 1/k.

    If you can't remember the transformations, try considering the graphs of  y = x^2 (for translations and reflections) and  y = sinx for stretches. Works for me.

    (You seem to have got negged for no reason, so here's a free rep back )
    Haha, thanks for the rep, you can have some yourself
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Has a teacher ever helped you cheat?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Write a reply...
    Reply
    Hide
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.