Graphing a Mixed Piecewise Function

00:00 5 marks

Consider the function f defined by

\( f(x) = \begin{cases}
|x – 2|, & \text{if } x < 3 \\
\cos(x), & \text{if } x \geq 3
\end{cases}\)

Sketch the graph of f(x) and describe the continuity of the function at \(x=3\).

Hint Hint

Hint

Check the function values from both sides of x = 3 to determine continuity.

Answer Answer
Mark Scheme Mark Scheme
Explanation Explanation
Examiner Tips Examiner Tips
Common Errors Common Errors
Real World Context Real World Context
Focus Focus
Formula Booklet

Answer Answer

Complete Answer

The function f(x) is discontinuous at x = 3 because the left-hand limit (|3 – 2| = 1) does not equal the function value from the right (cos(3) \(~ -0.99\)). This results in a jump discontinuity at x = 3.

Mark Scheme Mark Scheme

Answer Explanation Answer Explanation

Examiner Tips Examiner Tips

Common Errors Common Errors

Focus Focus

Formula Booklet