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