Function Notation and Linear Functions

Key Questions

  • How do you write linear equations in function notation?

    First, convert the linear equation to slope-intercept form. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)#

    Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value.

    Then switch out the #y# variable for #f(x)#:

    #f(x) = mx + b#

    smendyka · 1 · Jun 23 2018
  • What is a function?

    Answer:

    A function is a set of ordered pairs (points) formed from a defining equation, where, for each #x#-value there is only one #y#-value.

    Explanation:

    #x-------> y# represents a function

    This means that you can choose an #x#-value and plug it into an equation, usually given as:

    #y= ....." " or" " f(x)= .....#

    This will give you a #y#-value.

    In a function there will be only ONE possible answer for #y#.

    If you find you have a choice, then the equation does not represent a function.

    The following are functions:

    #y=-3#

    #y=3x-5#

    #y = 2x^2-3x+1#

    #(1,2), (2,2), (3,2),(4,2)#

    The following are NOT functions:

    #x= 3#

    #y=+-sqrt(x+20)#

    EZ as pi · 1 · Mar 25 2018
  • What is an example of a linear equation written in function notation?

    We can do more than giving an example of a linear equation: we can give the expression of every possible linear function.

    A function is said to be linear if the dipendent and the indipendent variable grow with constant ratio. So, if you take two numbers #x_1# and #x_2#, you have that the fraction #{f(x_1)-f(x_2)}/{x_1-x_2}# is constant for every choice of #x_1# and #x_2#. This means that the slope of the function is constant, and thus the graph is a line.

    The equation of a line, in function notation, is given by #y=ax+b#, for some #a# and #b \in \mathbb{R}#.

    KillerBunny · 1 · Feb 1 2015

Questions

Graphs of Linear Equations and Functions