Step 4: Place “h” - the difference you found in Step 1 - into the rule from Step 3: Y = f(√(x) + h) shifts h units to the left Step 3: Place your base function (from the question) into the rule, in place of “x”: Step 1 for this example was positive (+ 1), so that’s rule 1: Step 2: Choose a rule based on whether Step 1 was positive or negative: The difference between the equations is a “+ 1”.

Step 1: Compare the right sides of both equations and note any differences: Example QuestionsĮxample question #1: How are the graphs of y = √(x) and y = √(x + 1) related? The following graph shows the base function f(x) = x 2 and the two “new” graphs created when we added 2 or subtracted 2.īase graph x 2 is shifted to the left (x 2 + 2) and to the right (x 2 – 2). Example of a Horizontal ShiftĪ horizontal shift of the function f(x) = x 2 of 2 units (i.e. Positive values of h shift in the negative direction along the number line and negative h values shift the positive direction. Look carefully at what the positive or negative added value h is doing: it’s the opposite of what you might expect. y = f(x – h) shifts h units to the right,.y = f(x + h) shifts h units to the left,.

The basic rules for shifting a function along a horizontal (x) are: Rules for Horizontal Shift of a Function Transformations > What is a Horizontal Shift of a Function?Ī horizontal shift adds or subtracts a constant to or from every x-value, leaving the y-coordinate unchanged. Feel like 'cheating' at Calculus? Check out our Practically Cheating Calculus Handbook, which gives you hundreds of easy-to-follow answers in a convenient e-book.

Horizontal shift