Example 2 from Algebra and Trigonometry, 3.5 Transformation of Functions

Shifting a Tabular Function Vertically

A function $f (x)$ is given in Table 2. Create a table for the function $g (x) = f (x) - 3.$

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

Table 2

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 $g (x) = f (x) - 3$ tells us that we can find the output values of $g$ by subtracting 3 from the output values of $f .$ For example:

$\begin{matrix} f (2) & = & 1 & Given \\ g (x) & = & f (x) - 3 & Given transformation \\ g (2) & = & f (2) - 3 \\ = & 1 - 3 \\ = & - 2 \end{matrix}$
Subtracting 3 from each $f (x)$ value, we can complete a table of values for $g (x)$ as shown in Table 3.

$x$ 2 4 6 8

$f (x)$ 1 3 7 11

$g (x)$ −2 0 4 8

Table 3

Your turn

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

The function $h (t) = - 4.9 t^{2} + 30 t$ gives the height $h$ of a ball (in meters) thrown upward from the ground after $t$ seconds. Suppose the ball was instead thrown from the top of a 10-m building. Relate this new height function $b (t)$ to $h (t),$ and then find a formula for $b (t) .$

How did it go?

Your turn

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

Solution

Your turn

Solution

Your turn