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Graph the Following Piecewise Functions:

Exercise 1

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Exercise 4

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Exercise 5

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Exercise 6

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Exercise 7

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Exercise 8

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Exercise 9

Find the analytical expression of the function.

Solution of exercise 1

Graph the piecewise function:

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Solution of exercise 4

Graph:

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Solution of exercise 7

Graph:

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Solution of exercise 8

Graph the function:

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Solution of exercise 9

Find the analytical expression of the function.

$\text{[math]}$ f(x) = \left\{\begin{matrix} -x \qquad if \qquad x <0\\ 1 \qquad if \qquad x = 0 \\ x \qquad if \qquad 0

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Kourtney Sison

August 2026

I get it somehow, there are others who are unfamiliar and I have a hard time with it but it’s okay that I get it.

Vanessa - Editorial Manager Superprof UK

September 2026

Thanks for sharing your thoughts! It’s completely normal to find some parts unfamiliar or more difficult than others. The important thing is that you’re making progress and understanding more as you practise. Keep going! 😊

At least I understood some of it, but there are others that I’m confused about and have a hard time understanding, but I get it.

Thanks for sharing! It’s great that you’ve understood some of it already. Don’t worry if a few parts are still confusing — keep practising and take your time with the trickier sections. You’ll get there! 😊

Normina Mangogawan

The lesson was a little difficult for me, especially the word problems, but the examples helped me understand it better.

Thanks for your feedback! Word problems can definitely be tricky, so we’re glad the examples helped make the lesson clearer. Keep practising — it gets easier with time! 😊

Kourtney Sison /Normina Mangogawan

Thankyouuu po

Piecewise Functions Worksheet

Graph the Following Piecewise Functions:

Exercise 1

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Solution of exercise 1

Solution of exercise 4

Solution of exercise 7

Solution of exercise 8

Solution of exercise 9

Theory

Exponent Rules

Composition of Functions

Constant Functions

Convergent and Divergent Sequences

Even and Odd Functions

Exponential Function

Graphing Parabolas

Arithmetic Sequence

Mean Value Theorem

Rolle’s Theorem

Intervals of Increase and Decrease

Periodic Functions

Graphing rational function I

Graphing rational function III

Inflection Points

Increasing and Decreasing Functions

Piecewise Functions

Trigonometric Functions

Linear Function Problems

Domain of a Function

Maxima, Minima and Inflection Points

Radical Functions

Function

Geometric Sequence

Coordinates of X Intercept Explained: GCSE and A Level

Bounded Sequence: Monotonic and Non-Monotic

L’Hôpital’s Rule

Graphing polynomial function I

Types of Functions

Coordinates in the Plane

Optimization

nth Term

Graphing rational function V

Limit of a Sequence

Absolute Value Function

Sequences

Geometric Sequence Problems And Solutions

Arithmetic Sequence Problems with Solutions

Logarithmic Functions

Concave and Convex Functions: Theory and Examples

Rational Functions: Graphs, Hyperbolas and Asymptotes Explained

Bounded Function Examples: Theory and Practice Questions

Maxima and Minima Examples With Solutions

Asymptote Functions: Theory and Practice Problems

Absolute Maxima Explained: Master Max/Min On Intervals

Inverse Function Explained: Simple Steps for A-Level Maths

Graphs of Quadratic Equations: Practice Questions and Answers

Applying Limits in Math: Limit Laws Made Clear

Monotone Sequences: Theory and Exercises

Linear Functions Worksheet With Solutions

Formulas

Sequence Formulas | Arithmetic, Geometric and More

Exercises

Inflection Points Worksheet

Sequences Problems

Concavity and Convexity Worksheet

Increase and Decrease Worksheet

Limit of Sequence Problems

Applications of Derivatives Worksheet

Exponential, Logarithmic and Trigonometric Functions Worksheet

Mean Value Theorem Word Problems

Rational Functions Worksheet

L’Hopital’s Rule Problems

Even and Odd Functions Worksheet

Asymptotes Worksheet