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Exercises Functions

Example 14 from Algebra and Trigonometry, 3.5 Transformation of Functions

Finding a Vertical Compression of a Tabular Function

A function $f$ is given as Table 10. Create a table for the function $g (x) = \frac{1}{2} f (x) .$

$x$	2	4	6	8
$f (x)$	1	3	7	11

Table 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
The formula $g (x) = \frac{1}{2} f (x)$ tells us that the output values of $g$ are half of the output values of $f$ with the same inputs. For example, we know that $f (4) = 3.$ Then

$g (4) = \frac{1}{2} f (4) = \frac{1}{2} (3) = \frac{3}{2}$
We do the same for the other values to produce Table 11.

$x$ $2$ $4$ $6$ $8$

$g (x)$ $\frac{1}{2}$ $\frac{3}{2}$ $\frac{7}{2}$ $\frac{11}{2}$

Table 11

Your turn

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

A function $f$ is given as Table 12. Create a table for the function $g (x) = \frac{3}{4} f (x) .$

$x$	2	4	6	8
$f (x)$	12	16	20	0

Table 12

How did it go?

PreviousGraphing a Vertical Stretch Next Recognizing a Vertical Stretch

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.