Analyzing Key Features of Graphs
A Grade 12 math worksheet focusing on identifying and interpreting key features of various functions from their graphs, including domain, range, intercepts, symmetry, and end behavior.
Includes
Standards
Topics
Analyzing Key Features of Graphs
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Date:
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Read each question carefully and provide the best answer based on your understanding of key features of graphs. Show all your work where applicable.
For the graph of the function f(x) shown below, identify the following key features:
1. Domain:
2. Range:
3. x-intercept(s):
4. y-intercept(s):
5. Interval(s) where the function is increasing:
6. Interval(s) where the function is decreasing:
7. Relative maximum(s) (coordinates):
8. Relative minimum(s) (coordinates):
9. Which of the following describes the end behavior of the function f(x) = -x³ + 2x² - 5?
As x → ∞, f(x) → ∞; as x → -∞, f(x) → -∞
As x → ∞, f(x) → -∞; as x → -∞, f(x) → ∞
As x → ∞, f(x) → ∞; as x → -∞, f(x) → ∞
As x → ∞, f(x) → -∞; as x → -∞, f(x) → -∞
10. A function is considered to be even if it is symmetric with respect to the:
x-axis
y-axis
origin
Line y = x
11. A function can have more than one y-intercept.
True
False
12. If a function is symmetric with respect to the origin, it is an even function.
True
False
13. Describe in your own words what the 'domain' and 'range' of a function represent.
14. Explain the difference between a relative maximum and an absolute maximum.
15. A vertical asymptote occurs at values of x where the function is .
16. The of a function tells us where the graph approaches as x approaches positive or negative infinity.