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Interpreting Horizontal versus Vertical Shifts · Physics Playground

Exercises Functions

Example 6 from Algebra and Trigonometry, 3.5 Transformation of Functions

Interpreting Horizontal versus Vertical Shifts

The function $G (m)$ gives the number of gallons of gas required to drive $m$ miles. Interpret $G (m) + 10$ and $G (m + 10) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$G (m) + 10$ can be interpreted as adding 10 to the output, gallons. This is the gas required to drive $m$ miles, plus another 10 gallons of gas. The graph would indicate a vertical shift.

$G (m + 10)$ can be interpreted as adding 10 to the input, miles. So this is the number of gallons of gas required to drive 10 miles more than $m$ miles. The graph would indicate a horizontal shift.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given the function $f (x) = \sqrt{x},$ graph the original function $f (x)$ and the transformation $g (x) = f (x + 2)$ on the same axes. Is this a horizontal or a vertical shift? Which way is the graph shifted and by how many units?

How did it go?

PreviousIdentifying a Horizontal Shift of a Toolkit Function Next Graphing Combined Vertical and Horizontal Shifts

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.5, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Solution

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