How Do You Translate a Function?

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

  • select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems

      • What Does Absolute Value Mean?What Does Absolute Value Mean?

      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!

  • Evaluate functions, expressed in function notation, given one or more elements in their domains

      • What is Function Notation?What is Function Notation?

      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.

  • Determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, ax + by = c, and y - y1 = m(x - x1)

      • What's a Function?What's a Function?

      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!

  • Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry

      • What is a Quadratic Function?What is a Quadratic Function?

      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 the functions f(x)=√x, f(x)=1/x, f(x)=x3, f(x)= 3√x, f(x)=bx, f(x)=|x|, and f(x)=logb (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval

      • What is an Absolute Value Function?What is an Absolute Value Function?

      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!

  • Determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d