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)y=mx+b

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

    Then switch out the yy variable for f(x)f(x):

    f(x) = mx + bf(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 xx-value there is only one yy-value.

    Explanation:

    x-------> yx−−−−−−→y represents a function

    This means that you can choose an xx-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