Honors Algebra: Domain and Range Practice
10 Problems • Medium Difficulty • Includes Graph-Based Questions
Name: ______________________________
Date: ______________
Class: ____________
Instructions: For each function below, find the domain and range. Write your answers using interval notation. For
problems that include a graph, use the graph to determine the domain and range — pay close attention to open
and closed circles and to dashed asymptote lines. Show any supporting work in the space provided.
1. f(x) = √(2x + 5)
Domain: _______________________________
2. f(x) = 1 / (x² − 9)
Range: _______________________________
(find the domain only)
Domain: _______________________________
3. f(x) = −2x² + 8x − 5
Hint: find the vertex first.
Domain: _______________________________
Range: _______________________________
4. f(x) = √(16 − x²)
Domain: _______________________________
Range: _______________________________
5. g(x) = (x² − 1) / (x − 1)
Hint: simplify first — watch for a hole in the graph.
Domain: _______________________________
Range: _______________________________
6. The graph below shows a piecewise function. Use the graph to determine its domain and range. Pay
attention to the open and closed circles.
Domain: _______________________________
Range: _______________________________
7. The graph below shows a parabola that continues indefinitely in the directions shown by the arrows.
Use the graph to determine its domain and range.
Domain: _______________________________
8. h(x) = 4 / (x² + 2)
Range: _______________________________
(find the range only — the domain is all real numbers)
Range: _______________________________
9. f(x) = |2x − 5| − 3
Domain: _______________________________
Range: _______________________________
10. The graph below shows a rational function with a vertical asymptote at x = 2 and a horizontal
asymptote at y = 1 (shown as dashed lines). Use the graph to determine its domain and range.
Domain: _______________________________
Range: _______________________________