TOPIC 2: TRANSFORMATIONS

Question 1

3 Geometrical Transformations

Answer 1

Translation
Scaling
Reflection

Question 2

Recommended order for translation and scaling

Answer 2

TSST

x: Translate, then Scale
y: Scale, then Translate

Question 3

y = |f(x)| VS y = f(|x|)

Answer 3

y = |f(x)| –> Reflect everything below y-axis upwards

y = f(|x|) –> Reflect right side to left side as well

Question 4

Reciprocal Graphs

Answer 4

Asymptotes:
* x-intercept become vertical asymptote
* vertical asymptote become x-intercept
* oblique asymptote become y=0

Max/Min Points:
* Min/max point become max/min point
—
* y-values all become reciprocal values
—
* graph increasing –> graph decreasing
* towards infinity –> towards 0+ / 0-
* at asymptotes remain same

Question 5

Standard phrase for translation

Answer 5

Translation of the graph by x units in the positive/negative x/y direction

Question 6

Standard phrase for scaling

Answer 6

Scaling of the graph parallel to the x/y axis by a scale factor of x.

Question 7

Standard phrasing for reflection

Answer 7

Reflection of the graph in the x/y axis.