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Exercises Graphs and straight lines

Example 13 from Algebra and Trigonometry, 4.1 Linear Functions

Graphing by Using Transformations

Graph $f (x) = \frac{1}{2} x - 3$ using transformations.

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 equation for the function shows that $m = \frac{1}{2}$ so the identity function is vertically compressed by $\frac{1}{2} .$ The equation for the function also shows that $b = - 3$ so the identity function is vertically shifted down 3 units. First, graph the identity function, and show the vertical compression as in Figure 16.

Figure 16 The function, $y = x,$ compressed by a factor of $\frac{1}{2}$ .

Then show the vertical shift as in Figure 17.

Figure 17 The function $y = \frac{1}{2} x,$ shifted down 3 units.

Your turn

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

Graph $f (x) = 4 + 2 x$ using transformations.

How did it go?

PreviousGraphing by Using the y-intercept and Slope Next Matching Linear Functions to Their Graphs

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 4.1, 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.