Radical Functions: Solving Radical Equations and Inequalities

Estimate a Solution Using a Graph

You may also be given a graph of a radical equation and asked to estimate the value of the function given a certain x-value. As long as you can read the graph, you will be able to find this solution.

Let's look at an example. Analyze the following graph.

Graph of f of x is equal to square root of the quantity x plus one minus one

This is the graph of f of x equals the square root of the quantity x minus one, plus one. Suppose you want to find the approximate value of the function at x = 3. You are looking for f(3). One option is to substitute the value 3 in for x into the function, but since you are just looking for an approximation, you can also use the graph.

Point (three, two point four) on the graph of f of x is equal to square root of the quantity x plus one minus one

If you move straight up on the graph starting at x = 3, you will hit the function f of x equals the square root of the quantity x minus one, plus one at approximately f(3) = 2.4. Therefore, the solution of the function at x = 3 is about 2.4.