Transformation Of Graph Dse Exercise ◆

Mastering the Transformation of Graphs: A Complete DSE Exercise Blueprint

Exercise B: Short Answer (Function Equations)

Given ( f(x) = |x| ), write the equation for:

1. Shift right 4 units, then reflect in x-axis.
2. Compress vertically by factor ( \frac12 ), then shift left 3.
3. Reflect in y-axis, then shift up 1.

Answers:

1. ( y = -|x - 4| )
2. ( y = \frac12|x + 3| )
3. ( y = |-x| + 1 ) (same as ( y = |x| + 1 ) due to symmetry)

Question 2 (Stretches & Reflections)

Given ( f(x) = x^2 - 4 ). Find the equation of the transformed graph after: transformation of graph dse exercise

(a) Vertical stretch by factor 3.
(b) Horizontal compression by factor ( \frac12 ) (i.e., ( a=2 )).
(c) Reflection in the x‑axis, then shift up by 1 unit.

Exercise A: Multiple Choice (Conceptual)

1. Which transformation moves ( y = x^3 ) left 3 units and down 2?
   a) ( y = (x-3)^3 - 2 )
   b) ( y = (x+3)^3 - 2 )
   c) ( y = (x-3)^3 + 2 )
   d) ( y = (x+3)^3 + 2 ) Mastering the Transformation of Graphs: A Complete DSE

2. The graph of ( y = f(2x) ) compared to ( y = f(x) ) is:
   a) Stretched horizontally
   b) Compressed horizontally
   c) Stretched vertically
   d) Shifted right

3. If ( g(x) = -f(x) + 5 ), then the graph of ( f ) is:
   a) Reflected in x-axis and up 5
   b) Reflected in y-axis and up 5
   c) Reflected in x-axis and down 5
   d) Reflected in y-axis and down 5 Shift right 4 units, then reflect in x-axis

Answers: 1-b, 2-b, 3-a

Exercise C: Graph Sketching (Without plotting points)

For ( f(x) = x^2 - 4 ), sketch and describe:

1. ( f(x) + 2 )
2. ( f(x - 3) )
3. ( -f(x) )
4. ( 2f(x) )
5. ( f(2x) )

Key features to note:

• Original: parabola vertex (0, -4), x-intercepts at ±2.
• ( f(x) + 2 ): vertex (0, -2), x-intercepts? Solve ( x^2 - 2 = 0 ) → ( x = \pm\sqrt2 ).
• ( f(x-3) ): vertex (3, -4), x-intercepts at 1 and 5.
• ( -f(x) ): vertex (0, 4), opens down.
• ( 2f(x) ): vertex (0, -8), narrower.
• ( f(2x) = 4x^2 - 4 ): vertex (0, -4), but narrower horizontally (x-intercepts at ±1).

Week 1 — Translations & Reflections

Solution:

• Inside function: ( (x+2) ) → shift left by 2 units.
• Outside function: ( -5 ) → shift down by 5 units.
• Point transformation:
  Original ( x=1 ) → new ( x = 1 - 2 = -1 )
  Original ( y=1 ) → new ( y = 1 - 5 = -4 )
  Answer: Shift left 2, down 5; ( (-1, -4) ).