Example 8 from Algebra and Trigonometry, 3.5 Transformation of Functions

Identifying Combined Vertical and Horizontal Shifts

Write a formula for the graph shown in Figure 11, which is a transformation of the toolkit square root function.

Graph of a square root function transposed right one unit and up 2.

Figure 11

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 graph of the toolkit function starts at the origin, so this graph has been shifted 1 to the right and up 2. In function notation, we could write that as

$h (x) = f (x - 1) + 2$
Using the formula for the square root function, we can write

$h (x) = \sqrt{x - 1} + 2$

Your turn

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

Write a formula for a transformation of the toolkit reciprocal function $f (x) = \frac{1}{x}$ that shifts the function’s graph one unit to the right and one unit up.

How did it go?

Solution

Your turn

Solution

Your turn