Solve f(x) = k or f(x) > k from a graph
A standard method from More about graphs of functions: the steps and worked examples.
Steps
- Draw the horizontal line y = k.
- f(x) = k: read the x-values where the curve meets the line.
- f(x) > k: read the x-values where the curve is above the line.
- To solve f(x) = g(x), read where the two graphs cross.
Worked examples
Example 1: Use graphs to solve x² − 2x − 3 = x + 1.
The parabola y = x² − 2x − 3 and the line y = x + 1 meet where x² − 3x − 4 = 0, so at x = −1 and x = 4. Reading the graph should give the same values.
Example 2: NF: the graph of y = x² + 1 is translated 3 units to the left. Find the new equation and vertex.
"left 3" is f(x + 3): y = (x + 3)² + 1
vertex (0, 1) → (−3, 1)Example 3: NF: the graph of y = f(x) passes through (2, 5). Where is that point on y = f(x − 2) + 3?
Right 2 and up 3: (4, 8).
For the whole topic, read More about graphs of functions: key points, common mistakes and how the DSE tests it.