Name: Unit 1 Guided Notes / Study Guide
Functions: For every input, we have _________________
• Domain = _______ or _____________ ; Range = ___________ or ___________
• The _______________ function maps an input onto itself
• If a ________________________ crosses the graph in only _______ place, the graph is
_____________________
Practice: You are given the function f(x,y) = (2x, -2y). What is f(-1,-1)?
Composite Functions: Work from the ____________ out
Practice: If f(x, y) = (–y, –x) and g(x, y) = (x -1, –y), then what is f(g(7, 4)) ?
Transformations: Moving a shape/point along the coordinate plane
• ________________ transformations: image is ______________ to the pre-image
Translation = Slide or shift
Rule:
1. Translate ΔABC 4 units to the left and 1 unit up.
2. Write a rule to describe this function.
Rule:
Reflections = Flip or mirror image
Rules: rx-axis (x,y) =
ry-axis(x,y) =
ry=x(x,y) =
Reflect ΔABC over the line x = 2
Rotations = Turn or spin
Rules: R90(x,y) =
R180(x,y) =
R270(x,y) =
Rotate ΔABC by 270o.
Dilations = Grow or shrink
Rule:
Scale Factor = ___________
Dilate ΔABC by a scale factor of ½.
Name: Composite Transformations
• What coordinates will the function R180(rx-axis(3,2)) have?
•
What coordinates will the function ry-axis(T3,-1(-4, 1)) have?
Geometric Forms: Describes how shapes move along lines when they are transformed
• Translations move along ___________________ lines
• Reflections move along lines ____________________ to the ______________________________
• Rotations move along ___________________________
Similarity vs Congruence: congruent figures are EXACTLY the same
• Distance Formula:
Partner Practice
1. What coordinates will a point (2, -4) reflected
over the line y = x have?
3. Find the distance from point M(-3, 7) to point
P(4, -2).
2. The point A (–6, –2) has undergone the
transformation T-1, 4. Which point is the preimage
of A?
4. The point Q(-4, 6) is translated to the right 6
units and down 4 units.
a. Write an expression using the form
Th,k(x,y) = (x + h, y+k) to describe this translation.
b. Write the new coordinates for Q’.
5. Reflect the figure over the line x=1.
6. Translate triangle ABC to the right 5 units and
down 4 units. Write an expression using the form
Th,k(x,y) = (x + h, y+k) to describe this translation.