Questions
MAT135H5_F25_ALL SECTIONS 2.4 Preparation Check
Multiple choice
Which of the following statements are TRUE? (Select all that apply.)
Options
A.All trigonometric functions are continuous at every point in their domain
B.All polynomials are continuous at every point in
𝑅
.
C.All rational functions are continuous at every point in their domain
D.The function
𝑓
(
𝑥
)
=
5
𝑥
+
4
𝑥
2
−
3
is a rational function, and it is continuous at every point in
𝑅
.
E.All piecewise defined functions are continuous at every point in their domain
F.All polynomials are continuous at every point in their domain
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Step-by-Step Analysis
To evaluate which statements are TRUE, I’ll examine each option on its own terms and connect them to fundamental concepts about continuity.
Option 1: 'All trigonometric functions are continuous at every point in their domain.' Trigonometric functions like sin, cos, and tan are continuous wherever they are defined. Since their domains are all real numbers for sin and cos, and for tan it’s all real numbers except the points where the denominator cos(x) is zero, this statement is true because we are considering continuity ......Login to view full explanationLog in for full answers
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