Learn with Amar
Teaching video
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Grade 11 chapters and video availability01 · Read and understand
What you will learn
- Factor an input transformation to identify its center and scale.
- Justify the conclusion "The point (a,f(a)) becomes (a/2+2,f(a))" using the stated assumptions.
Before you start
Function graphs and substitution.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
How is y=f(2x−4) related to y=f(x)?
Why this math matters
Factor an input transformation to identify its center and scale. This worked micro-lesson connects a precise mathematical condition to a conclusion you can check. The transfer task asks you to change the setting and decide which parts of the reasoning still apply.
Set up the model
A useful answer starts with clear assumptions:
- f is any function for which the transformed inputs are allowed.
- Only the input is transformed.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Read a horizontal scale from the inside expression
PausedQuestion: Start with the question. Paused.
Question
Start with the question
How is y=f(2x−4) related to y=f(x)?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Build the model
2x−4=2(x−2)
Factoring separates the horizontal shift from the input scaling.
Work through the mathematics
If the original point has input a, solve 2x−4=a
A graph point is located by matching its original function input.
Check the conclusion
The point (a,f(a)) becomes (a/2+2,f(a))
Horizontal distances are halved and then shifted two units right.
The result
The point (a,f(a)) becomes (a/2+2,f(a))
Horizontal distances are halved and then shifted two units right.
Common mistakes to catch
- Horizontal factors act reciprocally on graph coordinates.
- Do not read an unfactored inside constant as the shift.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Where does an original point (6,5) move?
Show a hint
Substitute a=6 into a/2+2.
Reveal answer and explanation
(5,5)
Its new input is 6/2+2.
Practice 2
Is the horizontal shift four units right?
Show a hint
Factor before reading the shift.
Reveal answer and explanation
No; it is two
The coefficient multiplying x also scales the constant inside.
Take the idea with you
Transform key points first when sketching a rescaled signal.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Make two formula pieces meet continuously
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