Algebra 2 Transformations of Functions Test with Point Values (PDF)

Algebra 2 math test: Transformations of Functions – Maths PDF

Cover of the book Algebra 2 Math Tests with Answer Keys (PDF)

Download as a PDFThe Algebra 2 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This algebra 2 transformations test for Algebra 2 covers transformations of functions (Common Core F-BF.B.3, F-IF.C.7), with a free PDF to print.

This 45-minute test on transformations of functions has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Transformations of Functions
Standards: F-BF.B.3, F-IF.C.7
Time: 45 minutes
Total: 20 points

Algebra 2 transformations test: questions

Question 1 – Describe a shift [2 pts]

Describe how \(g(x) = |x + 2| – 5\) differs from \(f(x) = |x|\) and name the vertex.

Question 2 – Write an equation [2 pts]

Write the equation of \(f(x) = x^{2}\) reflected over the x-axis and shifted up 4.

Question 3 – Transform a table [3 pts]

Values of f.

Use the table to find the points of \(g(x) = 2f(x + 1)\).

Question 4 – Equation from a graph [2 pts]

Graph of g (dashed: y = |x|).

The graph shows a transformation of \(f(x) = |x|\) (dashed). Write the equation of \(g\).

Question 5 – Even or odd [2 pts]

Determine whether each function is even, odd, or neither.

\(f(x) = x^{4} + 2x^{2}\) (1 point)
\(g(x) = x^{3} – 2x\) (1 point)

Question 6 – Domain and range [3 pts]

For \(g(x) = 2\sqrt{x – 3} – 4\), describe the transformations of \(\sqrt{x}\), find \(g(7)\), and state the domain and range.

Question 7 – Piecewise function [2 pts]

f(x) = x + 3 for x < 0 and f(x) = 3 - x for x ≥ 0.

The graph shows \(f(x) = x + 3\) for \(x < 0\) and \(f(x) = 3 - x\) for \(x \ge 0\). Find \(f(-4)\), \(f(0)\), and \(f(5)\).

Question 8 – Arch [2 pts]

A tunnel’s height is \(y = -(x – 4)^{2} + 16\) feet. Describe the transformations of \(y = x^{2}\) and find the maximum height and the width of the tunnel at the ground.

Question 9 – Find the error [2 pts]

Jamal says the graph of \(g(x) = f(x) – 4\) is the graph of \(f\) moved 4 units left. Explain the error and describe the correct shift.

Key facts behind this algebra 2 transformations test

Key facts

f(x) + k: up k; f(x – h): right h.
a·f(x): vertical stretch by |a|; negative a reflects over the x-axis.
f(bx): horizontal compression by 1/|b|; negative b reflects over the y-axis.
Even: f(-x) = f(x); odd: f(-x) = -f(x).
Piecewise functions use different rules on different intervals.

How to use this algebra 2 transformations test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

Voter.. post

Free printable PDF