Characteristics of Graphs Review
A Grade 12 math worksheet on identifying and analyzing key characteristics of various graphs, including domain, range, intercepts, symmetry, and end behavior.
Includes
Standards
Characteristics of Graphs Review
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Date:
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Read each question carefully and provide detailed answers, showing all work where applicable.
1. Consider the function f(x) = √(x - 3).
a) Determine the domain of f(x).
b) Determine the range of f(x).
2. Which of the following functions has both an x-intercept at (2,0) and y-intercept at (0,-4)?
y = 2x - 4
y = -2x + 4
y = x - 4
y = -x + 2
3. Which type of symmetry does the function y = x³ exhibit?
Symmetry about the x-axis
Symmetry about the y-axis
Symmetry about the origin
No symmetry
4. For the function f(x) = -2x⁴ + 3x² - 1, as x → ∞, f(x) → , and as x → -∞, f(x) → .
5. The end behavior of a rational function is determined by the of the numerator and denominator.
6. Analyze the characteristics of the graph shown below.
a) Domain:
b) Range:
c) x-intercept(s):
d) y-intercept(s):
e) Intervals where the function is increasing:
f) Intervals where the function is decreasing:
g) Relative maximum(s) (if any):
h) Relative minimum(s) (if any):
i) End behavior as x → ∞:
j) End behavior as x → -∞:
7. A function can have more than one y-intercept.
True
False
8. An even function is symmetric with respect to the y-axis.
True
False