Function Morph Quiz
Algebra II 30 Min • 30 Points Total
Function Morph Quiz
Name:
Date: Period:
Parent Functions:
\(f(x)=x^2\) \(f(x)=|x|\) \(f(x)=\sqrt{x}\) \(f(x)=x^3\)
Part I: Single Transformations & Identification (15 pts)
3 pts each
1. Translations: Given \(g(x) = |x - 5| + 3\), describe each shift relative to parent \(f(x) = |x|\).
/ 3 pts
Horizontal Shift:
Direction & Units:
Vertical Shift:
Direction & Units:
2. Reflections & Dilation: Consider \(g(x) = -\frac{1}{4}x^2\) transformed from parent \(f(x) = x^2\).
/ 3 pts
Reflection Axis:
Reflected over:
Dilation:
Type & Factor:
3. Multiple Choice: Which equation represents \(f(x) = \sqrt{x}\) reflected across the \(y\)-axis, then translated \(6\) units down?
/ 3 pts
A \(g(x) = -\sqrt{x} - 6\)
B \(g(x) = \sqrt{-x} - 6\)
C \(g(x) = \sqrt{-(x - 6)}\)
D \(g(x) = -\sqrt{x - 6}\)
4. Graph Identification: Solid parabola \(g(x)\) is transformed from dashed parent \(f(x) = x^2\).
/ 3 pts
x y
Vertex Coordinates:
Equation for \(g(x)\):
\(g(x) =\)
5. Inside vs. Outside Dilations: Classify transformations applied to parent \(f(x) = x^3\).
/ 3 pts
Function
Horizontal or Vertical?
Stretch / Compression & Factor
\(g(x) = (3x)^3\)
\(h(x) = 3x^3\)
Algebra II • Unit 2: Function Transformations Page 1 of 2 Turn page for Part II →
Function Morph Quiz • Page 2
Student Name:
Part II: Combined Transformations & Modeling (15 pts)
3 pts each
6. Multi-Step Sequence: Given \(g(x) = -2(x + 4)^2 - 7\), list all three distinct transformations from parent \(f(x) = x^2\) in logical order.
/ 3 pts
7. Verbal to Equation: Parent \(f(x) = \sqrt{x}\) undergoes these transformations in order:
/ 3 pts
• Stretch vertically by \(5\) • Reflect over \(x\)-axis • Shift right \(8\) units • Shift down \(3\) units
Final Equation: \(g(x) =\)
8. Coordinate Mapping: Point \((4, 2)\) is on \(f(x) = \sqrt{x}\). Find the corresponding image point on \(g(x) = 3f(x - 5) + 6\).
/ 3 pts
Show Mapping Rule & Calculations:
Image Point:
\((\) , \()\)
9. Error Analysis: A student claims \(g(x) = |x + 7| - 4\) shifts right \(7\) units because \(+7\) indicates positive motion.
/ 3 pts
Explain why this claim is incorrect:
Correct Shift:
10. Graphing & Key Features: Graph \(g(x) = -|x - 2| + 3\) on the grid and state the key attributes.
/ 3 pts
x y 2 4 -2 -4 2 4 -2 -4
Vertex:
Domain:
Range:
Algebra II • Unit 2: Function Transformations Page 2 of 2 Quiz End • Total Score: _____ / 30
Function Morph Answer Key
Teacher Solutions & Rubric Algebra II • 30 Points Total
Function Morph Quiz — Answer Key
Scoring: 10 Questions @ 3 pts
Part I: 15 pts | Part II: 15 pts
Grading Criteria:
Direction + Units = 1.5 pts each Dilation Type + Factor = 1.5 pts each Partial credit allowed where indicated
Part I: Single Transformations & Identification (15 pts)
Answers in Green
1. Translations: \(g(x) = |x - 5| + 3\) relative to parent \(f(x) = |x|\).
3 / 3 pts
Horizontal Shift (1.5 pts):
Shifted RIGHT 5 units
(1 pt for "Right", 0.5 pt for "5 units")
Vertical Shift (1.5 pts):
Shifted UP 3 units
(1 pt for "Up", 0.5 pt for "3 units")
2. Reflections & Dilation: \(g(x) = -\frac{1}{4}x^2\) transformed from \(f(x) = x^2\).
3 / 3 pts
Reflection (1.5 pts):
Reflected across the \(x\)-axis
(Negative sign is outside the parent function)
Dilation (1.5 pts):
Vertical compression by factor \(\frac{1}{4}\)
(Accept "vertical shrink by \(\frac{1}{4}\)")
3. Multiple Choice: \(f(x) = \sqrt{x}\) reflected across \(y\)-axis, then translated \(6\) units down.
3 / 3 pts
A \(g(x) = -\sqrt{x} - 6\)
B \(g(x) = \sqrt{-x} - 6\)
Correct
C \(g(x) = \sqrt{-(x - 6)}\)
D \(g(x) = -\sqrt{x - 6}\)
4. Graph Identification: Determine vertex and formula for solid parabola \(g(x)\).
3 / 3 pts
x y (-3, 2)
Vertex Coordinates (1 pt): \(h = -3, k = 2 \implies \mathbf{(-3, 2)}\)
Equation for \(g(x)\) (2 pts): \(\mathbf{g(x) = -(x + 3)^2 + 2}\) (1 pt for reflection \(-(x+3)^2\), 1 pt for \(+2\))
5. Inside vs. Outside Dilations: Classify transformations applied to parent \(f(x) = x^3\).
3 / 3 pts
Function
Horizontal or Vertical?
Stretch / Compression & Factor
\(g(x) = (3x)^3\)
Horizontal (0.5 pt)
Compression by factor \(\frac{1}{3}\) (1 pt)
\(h(x) = 3x^3\)
Vertical (0.5 pt)
Stretch by factor \(3\) (1 pt)
Algebra II • Unit 2: Function Transformations (Teacher Key) Page 1 of 2 Part II Answers on Page 2 →
Function Morph Quiz — Answer Key • Page 2
Part II Total: 15 Points
Part II: Combined Transformations & Modeling (15 pts)
3 pts each
