Characteristics of Graphs Worksheet

Explore and analyze the characteristics of various functions and their graphs, including domain, range, intercepts, symmetry, and end behavior.

Grade 11 Math Data and GraphingCharacteristics of Graphs

Use This Worksheet

Includes

Multiple ChoiceFill in the Blanks2 Short AnswerTrue / FalseGraph

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7CCSS.MATH.CONTENT.HSF.BF.B.3

Topics

mathgrade 11graphsfunctionscharacteristics

8 sections · Free to use · Printable

Characteristics of Graphs

Name:

Date:

Score:

Read each question carefully and provide clear, concise answers. Show all your work where applicable.

1. Which of the following describes the domain of the function f(x) = √(x - 3)?

x > 3

x < 3

x ≥ 3

All real numbers

2. A function is considered to have an even symmetry if:

f(x) = -f(x)

f(-x) = f(x)

f(-x) = -f(x)

The graph passes through the origin

3. The of a function is the set of all possible output values (y-values).

4. A graph has symmetry if it is unchanged when reflected across the y-axis.

5. Consider the function g(x) = (x^2 - 4) / (x - 2). Identify any holes or vertical asymptotes in the graph of g(x).

6. The end behavior of a polynomial function is determined by its leading term.

True

False

7. A horizontal asymptote exists for a rational function when the degree of the numerator is greater than the degree of the denominator.

True

False

8. For the graph of f(x) = x^3 - 9x, determine the x-intercepts, y-intercept, and discuss its symmetry.

9. Sketch the graph of a function that has a domain of (-∞, 4], a range of [-2, ∞), an x-intercept at (2,0), and a y-intercept at (0,1).