Precalculus Transformations of Graphs Test with Point Values (PDF)

Precalculus math test: Transformations of Graphs – Maths PDF

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This precalculus transformations test for Precalculus covers transformations of graphs (Common Core F-BF.B.3, F-IF.C.7b), with a free PDF to print.

This 20-point test covers shifts, reflections, stretches, even and odd functions and a modeling problem (F-BF.B.3). You have 45 minutes. Show your work.

Time and points

About this test

Grade: Precalculus
Chapter: Transformations of Graphs
Standards: F-BF.B.3, F-IF.C.7b
Time: 45 minutes
Total: 20 points

Precalculus transformations test: questions

Question 1 – Describe transformations [2 pts]

Describe the transformations that change \(y=x^{2}\) into \(y=-(x+2)^{2}+4\).

Question 2 – Move points [2 pts]

The point \((4,-3)\) is on \(f\). Find the matching point on (a) \(y=f(x-1)+2\); (b) \(y=-2f(x)\).

Question 3 – Write an equation [2 pts]

Write the equation of \(y=\sqrt{x}\) shifted left 4 and then reflected over the \(x\)-axis, and state its range.

Question 4 – Even and odd [2 pts]

Decide whether each is even, odd or neither: (a) \(f(x)=x^{3}-5x\); (b) \(g(x)=x^{2}+1\).

Question 5 – Read an absolute value graph [3 pts]

A transformation of y = |x|.

(a) Write the equation of the graph. (b) State the range. (c) Find the \(x\)-intercepts.

Question 6 – Transform a table [2 pts]

Values of f.

Complete a table for \(g(x)=2f(x)-1\) using the same \(x\)-values.

Question 7 – Sequence of transformations [2 pts]

Describe the transformations from \(y=\sqrt{x}\) to \(y=3\sqrt{x-2}+1\) and find the value at \(x=11\).

Question 8 – Fountain [3 pts]

Water from a fountain.

Water follows \(y=-0.5(x-4)^{2}+8\) (feet). (a) Find the greatest height. (b) Find the height when \(x=2\). (c) Find where it lands.

Question 9 – Order of transformations [2 pts]

Write the equation obtained from \(y=x^{2}\) by shifting right 3, stretching vertically by 2, and reflecting over the \(x\)-axis.

Key facts behind this precalculus transformations test

Key facts

f(x) + k shifts up k; f(x – h) shifts right h.
-f(x) reflects over the x-axis; f(-x) reflects over the y-axis.
a f(x) stretches vertically by |a|; f(bx) compresses horizontally by 1/|b|.
A point (p, q) on f becomes (p + h, a q + k) on a f(x – h) + k.
Even functions satisfy f(-x) = f(x); odd functions satisfy f(-x) = -f(x).

How to use this precalculus 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 Precalculus chapters: Precalculus math.

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