3.7 (text 1.8) Using Transformations to Graph PDF

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3. 3.7 7 Using T Tra ra ransformations nsformations to Gr Graph aph Functions (text 1.8) Unit 3: Introduction to Functions MCR3U1: Functions

Review of T Transf ransf ransformations ormations

y = a f [k (x - d)] + c VERTICAL TRANSFORMATIONS y =af(x) represents a compared to y = f(x) If |a| > 1, the graph of y = af(x) is If 0 < |a| < 1, the graph of y = af(x) is If a is negative, the graph of y = af(x) is y = f(x) + c represents a

compared to y = f(x)

If c > 0, the graph of y = f(x) + c is If c < 0, the graph of y = f(x) + c is

HORIZONTAL TRANSFORMATIONS y =f(kx) represents a compared to y = f(x) If |k| > 1, the graph of y = f(kx) is If 0 < |k| < 1, the graph of y = f(kx) is If k is negative, the graph of y = f(kx) is y = f(x - d) represents a

compared to y = f(x)

If d > 0, the graph of y = f(x - d) is If d < 0, the graph of y = f(x - d) is

Example 1: Given f(x) = -2(x + 3)2 – 4: a) Explain the transformations needed to create the new function from the parent function.

b) Does order matter when transforming functions? Explain.

Example 2: Write equations for the following transformations: a) Reciprocal function: left 3, down 1, vertical stretch by a factor of 8

b) Positive square root function: reflected in the y –axis, vertical compression by a factor of ½, horizontal stretch by a factor of 3, up 4, right 2

c) Quadratic function: down 2, left 1, reflected in the x-axis, horizontal compression by a factor of 1/3

Example 3: Match the equations below with the graphs to the right: 5 a) y  x  4 b) y   x  1  1 c) y  x  3  3 d) y  x  3  3

10

e) y  x  2  3

Example 4: Given:

and

a) What is the difference between the two functions?

b) Which form would you use to graph? Explain.

c) How would you write the functions below so they can be graphed easily?

Example 5: Graph the following functions using transformations. actor “k” to get k(x – d). IMPOR IMPORT TANT ANT:: Make sure to ffactor a) f(x) = -½(2x – 4)2 - 3 Parent x

Transformed x

b) f(x) = 2  Parent x

c) y = Parent x

1 x 2 2

Transformed f(x)

+ 1

Transformed x

2   3 x  6

Parent f(x)

Parent f(x)

Transformed f(x)

Parent f(x)

Transformed f(x)

- 1

Transformed x

Practice: pg. 70 #1-3, 5c, (6-9)b, 16, 18...