Transformations of Linear Functions
I can write a shifted, stretched or flipped line and tell which way it moves.
What students learn
Students learn to write g(x) from f(x) for a shift, stretch or flip, and test a point to tell which way the graph moves.
See inside
The key rule
A number added outside f( ) moves the graph up or down; a number added inside moves it left or right, the opposite way to its sign.
f(x − h): right h
For a left/right shift, test a point: if g(6) gives what f(0) gave, the shift is right 6.
Watch out
f(x) = x + 5. A student says g(x) = f(x − 4) moves the graph left 4.
The mistake: left 4: the sign is −The sign inside works on the input, not the direction.
The fix: right 4: g(4) = f(0) = 5x must be 4 bigger to give the same output.
The mistakes it targets
- Reads a minus inside the parentheses as a shift left
- Multiplies only the slope when stretching every output
- Calls a change in slope a shift
- Lets a minus in front reach only the first term
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.