How Do You Translate a Function?

Note:

Think about sliding a penny on a table. All you're doing is moving the penny to a new location on the table. That's basically all that's happening when you translate a function! When you translate a function, you're just sliding it to a new location on the coordinate plane!

Keywords:

problem
translate
translation
vertical
horizontal
up
down
left
right
slide
function
move
graph

Background Tutorials

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation.
- What Does Absolute Value Mean?
  
  In this tutorial you'll see how you can think of absolute value in a very intuitive way. Let us know if you have any questions about it!
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
- What's a Function?
  
  You can't go through algebra without learning about functions. This tutorial shows you a great approach to thinking about functions! Learn the definition of a function and see the different ways functions can be represented. Take a look!
Lines are taken to lines, and line segments to line segments of the same length.
- What is a Transformation?
  
  Transformations can be really fun! They allow you to change or move a figure. In this tutorial, learn about all the different kinds of transformations!
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
- What is Function Notation?
  
  Every see 'f(x)' in your math? That's function notation! It's a way to indicate that an equation is a function. Learn about function notation by watching this tutorial.
Graph linear and quadratic functions and show intercepts, maxima, and minima.
- What is a Quadratic Function?
  
  You can't go through algebra without seeing quadratic functions. The graphs of quadratic functions are parabolas; they tend to look like a smile or a frown. In this tutorial, get introduced to quadratic functions, look at their graphs, and see some examples of quadratic functions!
Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- What is an Absolute Value Function?
  
  An absolute value function is just a function that contains absolute values. This tutorial gives a great introduction to this very useful function!
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
- What Does the Constant 'h' do in y = |x-h|?
  
  When you're learning about translating absolute value equations, learning about horizontal translations is a MUST! Check out this tutorial and see what it takes to translate an absolute value equation horizontally.
- What Does the Constant 'k' Do in the Function f(x)=[square root of](x)+k?
  
  When you're learning about translating square root functions, learning about vertical translations is a MUST! Check out this tutorial and see what it takes to translate a square root function vertically.