How Do You Horizontally Translate a Square Root Function?

How Do You Horizontally Translate a Square Root Function?

Note:

When you're learning about translating square root functions, learning about horizontal translations is a MUST! Check out this tutorial and see what it takes to translate a square root function horizontally.

Keywords:

  • square root function transformation
  • square root transformation
  • square root function
  • transformation

Background Tutorials

  • Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

      • What's a Perfect Square?What's a Perfect Square?

      What's a Perfect Square?

      Anytime you square an integer, the result is a perfect square! The numbers 4, 9, 16, and 25 are just a few perfect squares, but there are infinitely more! Check out this tutorial, and then see if you can find some more perfect squares!

  • Lines are taken to lines, and line segments to line segments of the same length.

      • What is a Translation?What is a Translation?

      What is a Translation?

      Ever slide something across a table? If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples. Take a look!

  • 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 Domain?What is Domain?

      What is Domain?

      Did you know that a relation has a domain? The domain of a relation is the set of the first coordinates from the ordered pairs. This tutorial defines the domain of a relation!

Further Exploration

  • 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.