Grade 11 · Algebra & functions

Function transformations practice

Function transformations is a grade 11 math skill aligned to Common Core standard HSF.BF.B.3: identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(kx), and f(x + k) for specific values of k. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 20 function transformations problems our math games drill.

CCSS HSF.BF.B.320 questions in the bank
Sample questions

Try 8 for free

Question 1easy

How does the graph of y=f(x+4)y = f(x + 4) compare to y=f(x)y = f(x)?

x+4x + 4 means x−(−4)x - (-4), so the graph shifts left 44.

Question 2easy

How does the graph of y=−f(x)y = -f(x) compare to y=f(x)y = f(x)?

The negative sign in front of ff reflects the graph over the xx-axis.

Question 3easy

The graph of y=f(x+4)−2y = f(x + 4) - 2 is the graph of y=f(x)y = f(x) shifted left by how many units?

A shift left of 44 unit(s) follows from the transformation y=f(x+4)−2y = f(x + 4) - 2.

Question 4easy

How does the graph of y=2f(x)y = 2f(x) compare to y=f(x)y = f(x)?

Multiplying f(x)f(x) by 22 stretches the graph vertically by a factor of 22.

Question 5easy

How does the graph of y=f(x)−5y = f(x) - 5 compare to y=f(x)y = f(x)?

Subtracting 55 outside the function shifts the graph down 55.

Question 6easy

The graph of y=f(x−6)+1y = f(x - 6) + 1 is the graph of y=f(x)y = f(x) shifted right by how many units?

A shift right of 66 unit(s) follows from the transformation y=f(x−6)+1y = f(x - 6) + 1.

Question 7easy

The graph of y=f(x+2)+7y = f(x + 2) + 7 is the graph of y=f(x)y = f(x) shifted left by how many units?

A shift left of 22 unit(s) follows from the transformation y=f(x+2)+7y = f(x + 2) + 7.

Question 8easy

The graph of y=f(x−8)−3y = f(x - 8) - 3 is the graph of y=f(x)y = f(x) shifted right by how many units?

A shift right of 88 unit(s) follows from the transformation y=f(x−8)−3y = f(x - 8) - 3.

Tests that cover function transformations:
SATACTPARCCNC EOG/EOCNY State Math
More Grade 11 skills:
Exponential and log formulasGeometric sequence equationsComplex number operationsLogarithm rulesBinomial theorem and factorialsConic sectionsSequences and seriesAll Grade 11 practice →

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