Home / Worksheets / Grade 11 / Math / Grade 11 Math: Function Characteristics

Grade 11 Math: Function Characteristics

Identify intercepts, symmetry, domain, range, and end behavior. Includes a worked example, printable practice, and an answer key with explanations.

Make a version for your classChange the level, length or topic and get a new worksheet with an answer key in about a minute. Free to try, no account needed.
Grade 11 Math AlgebraFunctionsFunction Characteristics

The answer key follows the practice below. In the editor, remove the final answer-key section before sharing a student copy.

Use This Worksheet

Includes

2 Text2 Short AnswerMultiple ChoiceTrue / FalseFill in the Blanks

Standards

CCSS.MATH.CONTENT.HSF.IF.B.4CCSS.MATH.CONTENT.HSF.IF.C.7

Topics

functionsalgebraprecalculuscharacteristicsgrade11
9 sections · Free to use · Printable
← More Math worksheets for Grade 11

Function Characteristics Worksheet

Name:

Date:

Score:

Learning goal and worked example

Identify intercepts, symmetry, domain, range, and end behavior.

For y = |x+1|−2, the vertex is (−1,−2), the range is [−2,∞), and solving |x+1|=2 gives x-intercepts −3 and 1.

To find a y-intercept, substitute x=0; to find x-intercepts, solve y=0. Check whether the equation can actually reach zero.

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. The graph shows y = x² - 4. The parabola continues beyond the viewing window. Determine its domain and range.

y = x² - 4 (continues beyond the window)-5-5-4-4-3-3-2-2-1-1001122334455y = x² - 4 (continues beyond the window)xy

Domain:  

Range:  

2. Which of the following functions has an x-intercept at (3, 0)?

a

f(x) = 2x + 6

b

f(x) = x - 3

c

f(x) = x^2 + 9

d

f(x) = 3x

3. The function f(x) = x^3 is an even function.

T

True

F

False

4. For the function f(x) = -x^4 + 2x^2 - 1, as x approaches positive infinity, f(x) approaches  , and as x approaches negative infinity, f(x) approaches  .

5. Consider the function g(x) = |x - 2| + 1. Sketch its graph and identify the domain, range, and any intercepts.

-5-4-3-2-112345-5-4-3-2-112345

Domain:  

Range:  

X-intercept(s):  

Y-intercept(s):  

Answer key and worked solutions

1. For y=x²−4, domain ℝ and range [−4,∞).

2. b: f(3)=3−3=0. 3. False: x³ is odd since f(−x)=−f(x).

4. −∞ in both blanks; −x⁴ is the leading term.

5. V-shaped graph with vertex (2,1), points (1,2),(3,2),(0,3),(4,3). Domain ℝ; range [1,∞); no x-intercepts because values are at least 1; y-intercept (0,3).

Related Worksheets

Transforming Parabolas Worksheet

Use vertex form to describe and graph transformed parabolas. Includes a worked example, printable practice, and an answer key with explanations.

Solving Polynomial Equations Worksheet

Solve polynomial equations using factors, root candidates, and division. Includes a worked example, printable practice, and an answer key with explanations.

Zeros and Multiplicity Worksheet

Relate repeated factors to zeros and local graph behavior. Includes a worked example, printable practice, and an answer key with explanations.

Graphs of Polynomials

Use leading terms and multiplicity to sketch polynomial graphs. Includes a worked example, printable practice, and an answer key with explanations.

Solving Square Root Equations

Solve radical equations and reject extraneous candidates. Includes a worked example, printable practice, and an answer key with explanations.

Radical Operations Worksheet

Simplify and combine radicals, then rationalize denominators. Includes a worked example, printable practice, and an answer key with explanations.