Absolute Value Warmup Slides
Warm-Up 1
Absolute Value Transformations
Algebra 2 • Unit 2
x y -4 4 4 -4 O
Write an equation for the horizontal translation of \(y = |x|\) shown in the graph.
A \(y = |x - 3|\)
B \(y = |x + 3|\)
C \(y = -|x + 3|\)
D \(y = -|x - 3|\)
Focus: Horizontal shift & vertex coordinates Similar to Test Q6
Warm-Up 2
Absolute Value Transformations
Algebra 2 • Unit 2
Write the equation that is the translation of the parent function \(y = |x|\) shifted 4 units to the left and 5 units down.
A \(y = |x - 4| - 5\)
B \(y = |x + 4| + 5\)
C \(y = |x + 4| - 5\)
D \(y = |x - 5| + 4\)
Focus: Standard vertex form \(y = a|x - h| + k\) Similar to Test Q8
Warm-Up 3
Absolute Value Transformations
Algebra 2 • Unit 2
x y -3 3 3 -3 O
Which function represents the graph shown on the coordinate plane?
A \(y = -2|x| + 4\)
B \(y = 2|x| + 4\)
C \(y = -2|x| - 4\)
D \(y = -\frac{1}{2}|x| + 4\)
Focus: Vertical stretch factor & reflection across the x-axis Similar to Test Q9
Warm-Up 4
Absolute Value Transformations
Algebra 2 • Unit 2
x y 3 -3 3 O f(x) g(x)
Function: \(g(x) = \frac{1}{3}|x|\)
Which statement correctly describes the transformation from the parent function \(f(x) = |x|\) to \(g(x)\)?
A The graph of \(g\) is a vertical stretch of the parent function.
B The graph of \(g\) is a vertical shrink of the parent function.
C The graph of \(g\) is a horizontal translation \(\frac{1}{3}\) unit to the right.
D The graph of \(g\) is a reflection across the y-axis.
Focus: Vertical dilation terminology (\(0 < |a| < 1\) vs. \(|a| > 1\)) Similar to Test Q10
Warm-Up 5
Absolute Value Transformations
Algebra 2 • Unit 2
x y -3 3 3 -3 O f g
Write a function \(g\) whose graph represents the indicated transformation of \(f(x) = |x|\).
A \(g(x) = |x + 2| + 3\)
B \(g(x) = -|x + 2| + 3\)
C \(g(x) = -|x - 2| + 3\)
D \(g(x) = -|x + 3| + 2\)
Focus: Writing equations from reflected & translated graphs Similar to Test Q11
Warm-Up 6
Absolute Value Transformations
Algebra 2 • Unit 2
Compare the graph of \(f(x) = 3|x - 2| - 5\) to its parent function \(y = |x|\). Which statement is completely correct?
A Vertical stretch by factor of \(3\), translated \(2\) units right and \(5\) down; range is \(y \ge -5\).
B Vertical shrink by factor of \(\frac{1}{3}\), translated \(2\) units left and \(5\) down; range is \(y \ge -5\).
C Vertical stretch by factor of \(3\), translated \(2\) units left and \(5\) down; range is all real numbers.
D Vertical stretch by factor of \(3\), translated \(2\) units right and \(5\) up; range is \(y \ge 5\).
Focus: Complete transformation analysis & range identification Similar to Test Q18
Teacher Key
Answer Key & Test Question Alignment
Quick Reference
1. B
Aligned to Version A #6
Vertex at \((-3, 0)\). Horizontal translation left \(3\) units yields \(y = |x - (-3)| = |x + 3|\).
2. C
Aligned to Version A #8
Left \(4\) units gives \(|x + 4|\); down \(5\) units gives \(- 5\). Equation is \(y = |x + 4| - 5\).
3. A
Aligned to Version A #9
Opens downward (\(a < 0\)), vertical stretch \(2\) (slopes \(\pm 2\)), shifted up \(4\) to vertex \((0, 4)\).
4. B
Aligned to Version A #10
Because \(0 < \frac{1}{3} < 1\), the transformation is a vertical shrink, making the graph wider.
5. B
Aligned to Version A #11
Reflected over x-axis (\(-\)), vertex at \((-2, 3)\). Standard form: \(g(x) = -|x + 2| + 3\).
6. A
Aligned to Version A #18
Stretch factor \(3\), vertex \((2, -5)\) (right \(2\), down \(5\)). Minimum is \(-5\), so range is \(y \ge -5\).
Standard: TEKS 2A.4A, 2A.4B, 2A.6C (Absolute Value Transformations) Screenshots ready for LMS & Bellringers
