## f(x)=√x

### f(x) = √x is a function that represents the square root of x

f(x) = √x is a function that represents the square root of x.

To understand this function, let’s explain a few key points:

1. Domain: The domain of this function is the set of all non-negative real numbers because taking the square root of a negative number is undefined in the real number system. So, the domain is x ≥ 0.

2. Range: The square root of any non-negative number is always a non-negative number or zero. Therefore, the range of this function is y ≥ 0.

3. Intercepts: To find the x-intercept, we set y = 0 and solve for x. In this case, we get √x = 0, which means x = 0. So the function passes through the point (0, 0).

4. Graph: The graph of f(x) = √x is a curve that starts from the origin (0, 0) and extends infinitely in the positive x and y directions. It gradually increases as x increases. The graph never dips below the x-axis.

5. Symmetry: This function is not symmetric with respect to the y-axis or the origin. It only exhibits symmetry with respect to the y-axis. In other words, if (a, b) is on the graph, then (-a, b) is also on the graph.

6. Continuity: This function is continuous for all x-values in its domain. There are no discontinuities, jumps, or holes in the graph.

7. Increasing/Decreasing: The function is increasing for all x ≥ 0. As x increases, the square root of x also increases.

8. Behavior at x = 0: At x = 0, the square root is also 0. The function approaches 0 but never reaches negative values.

9. Operations: You can perform various operations on this function, such as addition, multiplication, composition, etc., to create new functions or transform the existing one.

## More Answers:

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