Results 1 to 8 of 8

Math Help - Equation of function

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    23

    Equation of function

    f is a linear function such that f(1) = 0 and f(2) = 4. How do you write an equation for f(x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    May 2009
    Posts
    471
    Quote Originally Posted by SHiFT View Post
    f is a linear function such that f(1) = 0 and f(2) = 4. How do you write an equation for f(x)

    I'm sure you heard somewhere along the line that linear functions can be written as y=mx+b or f(x)=mx+b


    So we have 2 points, and that's all we need. We use them to plug into that general formula

    0=m(1)+b and 4=m(2)+b

    Solve those two equations for m and b and you'll be able to write down your line y=mx+b
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    23
    I'm still confused though, so do I need to come up with two of my own points then solve, or do I just solve with the variables given?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    May 2009
    Posts
    471
    Quote Originally Posted by SHiFT View Post
    I'm still confused though, so do I need to come up with two of my own points then solve, or do I just solve with the variables given?

    You need to solve the following system of equations

    1. 0=m(1)+b and

    2. 4=m(2)+b




    Now let's try to get you to understand this. I hand you two points, (p,q) and (r,s) and say what's the equation of the line that goes through them

    You realize that all lines on the x-y plane can be written as y=mx+b

    So you also know that for the ordered pair (p,q), the x coordinate is p and the y coordinate is q.... same for (r,s)

    So since y=mx+b must be satisfied, you plug your points into in to get

    q=mp+b and

    s=mr+b

    Now in a normal problem p,q,r,s will be numbers so the only "unknowns" here are m and b

    You have two equations and 2 unknowns so you can solve for both m and b, and then the line you were looking for is y=mx+b


    Here they tell you f(1)=0 and f(2)=4, so since f(x)=y, the points they give you are (1,0) and (2,4)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by SHiFT View Post
    f is a linear function such that f(1) = 0 and f(2) = 4. How do you write an equation for f(x)
    Hi SHiFT,

    If f(1)=0, then the point is (1, 0).

    If f(2)=4, then the point is (2, 4)

    Find the slope using your two points.

    m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{2-1}=4

    Now, plug your slope of 4 and point (1, 0) into y=mx+b and find y-intercept b.

    0=4(1)+b

    b=-4


    y=4x-4

    \boxed{f(x)=4x-4}
    Last edited by masters; October 21st 2009 at 01:32 PM. Reason: Mild case of dyslexia as pointed out by Artvandalay11
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Banned
    Joined
    May 2009
    Posts
    471
    Quote Originally Posted by masters View Post
    Hi SHiFT,

    If f(1)=0, then the point is (0, 1). This is your y-intercept.

    If f(2)=4, then the point is (4, 2)

    Find the slope using your two points.

    m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-1}{4-0}=\frac{1}{4}

    Now, plug your slope and y-intecept into y=mx+b

    y=\frac{1}{4}x+1

    \boxed{f(x)=\frac{1}{4}x+1}


    We have 2 conditions, f(1)=0 and f(2)=4

    You gave \boxed{f(x)=\frac{1}{4}x+1}

    And if we compute f(1) we get \frac{1}{4}(1)+1=1.25\not = 0


    And if we compute f(2) we get \frac{1}{4}(2)+1=1.5\not=4

    You swapped your x and y's, meaning this function takes 0 to 1 and 4 to 2, you gave us the inverse of the function is question
    Follow Math Help Forum on Facebook and Google+

  7. #7
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    12
    Awards
    1
    Quote Originally Posted by artvandalay11 View Post
    We have 2 conditions, f(1)=0 and f(2)=4

    You gave \boxed{f(x)=\frac{1}{4}x+1}

    And if we compute f(1) we get \frac{1}{4}(1)+1=1.25\not = 0


    And if we compute f(2) we get \frac{1}{4}(2)+1=1.5\not=4

    You swapped your x and y's, meaning this function takes 0 to 1 and 4 to 2, you gave us the inverse of the function is question
    Excellent observation. I was just testing you.....I shall fix it straight away.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Sep 2009
    Posts
    23
    Thanks a ton guys, it makes a lot of sense now
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. function of y second order equation 2
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: November 22nd 2010, 06:20 AM
  2. Equation for a Function with Given Points
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 14th 2010, 11:46 PM
  3. Equation of a Function
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 26th 2009, 06:19 PM
  4. Equation of function
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 15th 2009, 12:50 AM
  5. Replies: 1
    Last Post: February 12th 2007, 03:40 PM

Search Tags


/mathhelpforum @mathhelpforum