IB Math SL Year 2
Name: _____________________
Date: ______________________
1-‐6 Transformations
Key Notes What do I need to know? Notes to Self 1. Transformations of Functions
• Definitions for: o Parent Function o Translation/shift o Reflection o Stretch/shrink o Compound Transformations
• Notation for: o See table below.
• Processes: o Graphically transform functions o Describe function transformations
*The following chart is a REFERENCE SHEET; the processes must be memorized!
In this lesson we will revisit the following learning goals: 1. How do we determine the graph and equation of a function when it is translated vertically? 2. Translated horizontally? 3 Reflected over the x-‐axis? Reflected over the y-‐axis? Stretched?
Fact Check!
• A ________________________________ is a shift of a function. • A stretch/shrink makes a function ____________________ or more ____________________.
• A reflection _______________________ a function across a given line (like a mirror image). • Compound transformations: more than ____________ transformation occurring on a _________________________
o Order of Performing Compound Transformations: “inside out” -‐-‐ the function is the “heart” and you peform closest to the “heart” and work your way out.
o Ex. y = -‐(x-‐1)2 + 9 ! 1st: right 1, 2nd: reflect over the x-‐axis, 3rd: up 9
Transformations f(x) notation Example Description Graph
Vertical Translation/Shift f(x) + c f(x) = |x|+ 3
IB Math SL Year 2
Horizontal Translation/Shift f(x -‐ c) f(x) = |x+3|
Vertical Stretch/Shrink cf(x) f(x) = 2|x|
Horizontal Stretch/Shrink f(cx) f(x) = |2x|
Reflection across x-‐axis -‐f(x) f(x) = -‐|x|
Reflection across y-‐axis f(-‐x) f(x) = |-‐x|
IB Math SL Year 2 Let’s Try Some Together!
1. Given the graph of 𝑦 = 𝑓(𝑥), sketch the graph of 𝑦 = 𝑓 𝑥 − 2 + 1.
2. Explain what transformation would occur to the function, 𝑓(𝑥) = 𝑥! if we did: y = f(x+1) – 4.
3. Given the graph of 𝑦 = 𝑓(𝑥), Sketch the graph of 𝑦 = 2𝑓(𝑥) Sketch the graph of 𝑦 = 𝑓(2𝑥)
You Try!
4. Let g(x) = f(x – 1). The point A(3, 2) on the graph of f is transformed to the point P on the graph of g. Find the
coordinates of P. 5. Given the graph of 𝑦 = !
! , sketch the graph of 𝑦 = !
!!!.
6. Given the graph of 𝑦 = !
! , explain what would happen to the graph of 𝑦 = −3 + !
!!!
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IB Math SL Year 2 7. The graph of the function y = f (x), 0 < x < 4, is shown below. On the diagram below, draw the graph of
y = 3f (−x).
8. Given the graph of 𝑦 = 𝑓(𝑥), Sketch the graph of 𝑦 = !
!𝑓(𝑥). Sketch the graph of 𝑦 = 𝑓(!
!𝑥)
9. Consider the following function: y = -‐3f(2x-‐6) + 9. Order the following transformation in the correct sequence that they would be performed:
_____ reflect over x-‐axis _____ vertical stretch of 3 _____ horizontal shrink of 2 _____ shift right 6 _____ shift up 9
10. Describe the translation of y=f(x) to y=g(x) that occurred. Then write this using your knowledge of transformations.
IB Math SL Year 2 11. The graph of the function f(x) = (x+1)2 + 4 is translated 2 unites to the right and 4 units up.
a. Find the function g(x) corresponding to the translated graph b. State the range of f(x) c. State the range of g(x).
12. The graph of a function 𝑔 is found by starting with the function 𝑓 𝑥 = !!, then applying the following
transformations: vertical stretch by a factor of 7, translation (shift) 5 units to the right, translation 3 units downwards. Write the function, g(x).
13. a. Use your GDC to sketch the graph of the function 𝑓 𝑥 = − 𝑥 + 2.
b. State the domain and range of 𝑓 in interval notation. c. Explain the transformations that occurred to f(x).
IB Math SL Year 2 14. Consider the function 𝑔 𝑥 = 2 + !
!!! .
a. Sketch the graph of 𝑔 for −3 ≤ 𝑥 ≤ 2.
b. For what value of 𝑥 is 𝑔 undefined?
c. Explain the transformation g(x) went under from the parent function, 𝑓 𝑥 = !!
d. Using your GDC, write down the value of the 𝑥-‐intercept and the 𝑦-‐intercept.
15. If f(x) = !!, find in simplest form,
a. f(-‐4) b. f(2x) c. f(!!) d. 4f(x+2) -‐ 4
Explain each transformation:
16. For the graph a y = h(x) given, sketch the graph of: *it might be useful to use different colors *label each graph by letter (a, b, c, d)
a. y = h(x) + 1 c. y = !!h(x)
b. y = h(-‐x) d. y = h(!
!)