Lesson 1 of 3
Move familiar points and distinguish input changes from output changes.
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Worked example · 1 of 8
Worked example
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A point lies on . On it becomes ; only the output moves.
Big ideas
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For , a point becomes . An outside addition changes the output while the input stays fixed.
For , a point becomes . Solve to locate the old input; h positive shifts right.
For , becomes , a reflection across the x-axis. For , it becomes , a reflection across the y-axis.
A horizontal shift changes the domain along with the graph; a vertical shift changes the range. Track endpoints and a second point, then verify using the formula.
Worked example
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For , the root endpoint moves from to . The source point becomes . Domain and range confirm the endpoint directions.
Step-through
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A point lies on . Locate its corresponding point on .
Whole picture, 4 steps
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Worked example
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Start with , whose domain and range are . For , solve : domain . The endpoint moves to , and the range is . Check .
Worked example
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The point on f becomes on , because the output changes sign. On , it instead becomes , because the input changes sign. The x-axis reflection keeps x; the y-axis reflection keeps y.
Mix-up alert
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Wrong idea: reflects a graph after moving it up 3. Repair: its output is first , then . Reflecting instead would give , a different formula.
Watch
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Flashcards
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Card 1 of 8
0 Know it0 Still learning
The addition acts on outputs.
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Where does f(x)+7 move a graph?
Up 7.
Where does f(x-5) move a graph?
Right 5.
Where does f(x+2) move a graph?
Left 2.
What reflection does make?
Across the x-axis.
What reflection does make?
Across the y-axis.
Where does (4,6) move under f(x)+1?
(4,7).
What is the endpoint of ?
(6,2).
How can you check an input shift?
Set the new inside expression equal to a known old input.
True or false
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Self-test
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6 questions. One at a time.
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Self-test
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6 questions. One at a time.
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