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Reflecting a Tabular Function Horizontally and Vertically · Physics Playground

Exercises Functions

Example 10 from Algebra and Trigonometry, 3.5 Transformation of Functions

Reflecting a Tabular Function Horizontally and Vertically

A function $f (x)$ is given as Table 6. Create a table for the functions below.

ⓐ $g (x) = - f (x)$
ⓑ $h (x) = f (− x)$

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

Table 6

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.

1
Solution
1. ⓐ
  For $g (x),$ the negative sign outside the function indicates a vertical reflection, so the x-values stay the same and each output value will be the opposite of the original output value. See Table 7.
  
  $x$ 2 4 6 8
  
  $g (x)$ –1 –3 –7 –11
  
  Table 7
2. ⓑ
  For $h (x),$ the negative sign inside the function indicates a horizontal reflection, so each input value will be the opposite of the original input value and the $h (x)$ values stay the same as the $f (x)$ values. See Table 8.
  
  $x$ −2 −4 −6 −8
  
  $h (x)$ 1 3 7 11
  
  Table 8

Your turn

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

A function $f (x)$ is given as Table 9. Create a table for the functions below.

ⓐ $g (x) = - f (x)$
ⓑ $h (x) = f (- x)$

$x$	−2	0	2	4
$f (x)$	5	10	15	20

Table 9

How did it go?

PreviousReflecting a Graph Horizontally and Vertically Next Applying a Learning Model Equation

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.

$x$	2	4	6	8
$g (x)$	–1	–3	–7	–11

$x$	−2	−4	−6	−8
$h (x)$	1	3	7	11

Solution

Your turn