Graph Features Analysis
Analyze and identify key features of various graphs including domain, range, intercepts, and intervals of increase/decrease.
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Graph Features Analysis
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Read each question carefully and analyze the provided graphs to determine the requested features. Write your answers in the space provided.
1. Consider the graph of the function f(x) = x². Identify the following features:
a. Domain:
b. Range:
c. x-intercept(s):
d. y-intercept(s):
e. Interval(s) where the function is increasing:
f. Interval(s) where the function is decreasing:
2. Which of the following statements is true about the x-intercepts of a function?
They are points where the graph crosses the y-axis.
They are points where y = 0.
They represent the maximum or minimum values of the function.
They are always positive.
3. True or False: A vertical asymptote occurs at x-values where the denominator of a rational function is zero and the numerator is non-zero.
True
False
4. The end behavior of a polynomial function describes the behavior of the graph of the function as x approaches positive or negative .
5. If a function has a horizontal asymptote at y = 3, this means that as x approaches positive or negative infinity, the y-values of the function approach .
6. Sketch a graph of a function that has a domain of (-∞, ∞), a range of [0, ∞), an x-intercept at (2,0), and is decreasing on (-∞, 2) and increasing on (2, ∞).