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Exercises Functions

Example 19 from Algebra and Trigonometry, 3.5 Transformation of Functions

Finding a Triple Transformation of a Tabular Function

Given Table 15 for the function $f (x),$ create a table of values for the function $g (x) = 2 f (3 x) + 1.$

$x$	6	12	18	24
$x$	10	14	15	17

Table 15

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
There are three steps to this transformation, and we will work from the inside out. Starting with the horizontal transformations, $f (3 x)$ is a horizontal compression by $\frac{1}{3},$ which means we multiply each $x -$ value by $\frac{1}{3} .$ See Table 16.

$x$ 2 4 6 8

$f (3 x)$ 10 14 15 17

Table 16

Looking now to the vertical transformations, we start with the vertical stretch, which will multiply the output values by 2. We apply this to the previous transformation. See Table 17.

$x$ 2 4 6 8

$2 f (3 x)$ 20 28 30 34

Table 17

Finally, we can apply the vertical shift, which will add 1 to all the output values. See Table 18.

$x$ 2 4 6 8

$g (x) = 2 f (3 x) + 1$ 21 29 31 35

Table 18

How did it go?

PreviousRecognizing a Horizontal Compression on a Graph Next Finding a Triple Transformation of a Graph

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.