Square Root Functions
Graph of y = √x translated and scaled.
Key idea
Graph of y = √x translated and scaled.
In depth
f(x) = √x is the inverse of x² restricted to x ≥ 0. Its domain begins where the radicand is zero, and it rises slowly with a vertical tangent at the start.
Worked example
f(x) = √(x − 1) + 2 begins at (1, 2) and passes through (2, 3) and (5, 4).
Formula
Real-world uses
- Modelling the time for an object to fall or the speed of waves in water depending on depth
Common mistake
Allowing negative inputs to the square root.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Square Root Functions?
Graph of y = √x translated and scaled. It is a topic at the advanced level in Algebra.
What is the formula for Square Root Functions?
The key formula is y = a√(x) + b.
Where is Square Root Functions used in real life?
Real-world examples: Modelling the time for an object to fall or the speed of waves in water depending on depth.
What should I learn before Square Root Functions?
Make sure you are comfortable with Rational Exponents, the previous topic in Algebra.
What is a common mistake with Square Root Functions?
Allowing negative inputs to the square root.
How can I practise Square Root Functions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Square Root Functions?
Move on to Piecewise Functions next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.