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Cogito

AP Precalculus · Chapter 4 · Lesson 1

Practice Worksheet

Transformations of Functions

Inside the bracket goes the wrong way.

11 problems · about 22 minutes · AP Precalculus 1.13, 1.14

NameDate

Figure — use these to answer the problems

Change a, b, and c and watch the parabola stretch and move.
-8-8-6-6-4-4-2-222446688
y = 1x² + 0x + 0
Vertical stretch a1
b0
Vertical shift c0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. f(x + 9) moves the graph left by how much?

    Answer

  2. f(x − 7). Right by how much?

    Answer

  3. f(x) + 2. Up by how much?

    Answer

  4. 3f(x). Vertical stretch factor?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Match each transformation to its effect.

    Draw a line from each item on the left to its match on the right.

    • f(x) + k
    • f(x + k)
    • −f(x)
    • f(−x)
    • Shift up by k
    • Shift left by k
    • Reflect across the x-axis
    • Reflect across the y-axis

  2. f(2x). Horizontal compression factor?

    Answer

  3. Order the steps for graphing y = 2f(x − 3) + 1 from the base graph.

    Write 1 to 3 in the boxes to put these in order.

    • Shift right 3
    • Stretch vertically by 2
    • Shift up 1

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. The point (2, 5) is on y = f(x). What is its y on y = f(x) + 4?

    Answer

  2. The point (2, 5) is on y = f(x). What is its x on y = f(x − 3)?

    Answer

  3. Inside the Bracket

    f(x + 4) moves the graph which way? Answer 1 for left, 2 for right.

    Answer

  4. Outside the Bracket

    f(x) − 6 moves the graph down by how much?

    Answer