Grade 12 Graph Features Worksheet
A worksheet for Grade 12 students focusing on identifying and interpreting key features of various graphs, including domain, range, intercepts, asymptotes, and intervals of increase/decrease.
Includes
Standards
Topics
Graph Features: Analysis and Interpretation
Name:
Date:
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Read each question carefully and analyze the given graphs or functions to determine their key features. Show all your work where applicable.
Consider the function f(x) = (x^2 - 4) / (x - 2).
1. What are the domain and range of f(x)? Explain any restrictions.
2. Identify any vertical or horizontal asymptotes for f(x).
3. The graph of a function is shown below. What is the approximate interval where the function is decreasing?
(-∞, -2)
(-2, 1)
(1, ∞)
(-∞, 1)
4. For the function g(x) = x^3 - 9x, the x-intercepts are , , and , and the y-intercept is .
5. A function can cross its horizontal asymptote.
True
False
6. A vertical asymptote occurs where the denominator of a rational function is zero, provided the numerator is not also zero at that point.
True
False
7. For the function h(x) = 3^(x-1) + 2, describe its end behavior and identify any asymptotes.