Let f(x) = {√x, 0 ≤ x ≤ 1

{ 1/x, x > 1

(a). Identify any intercepts
(b). Graph the function
(c). Find the domain and range

To identify any intercepts, we need to find the values of x for which f(x) equals zero.

(a). For the first part of the function, when 0 ≤ x ≤ 1, f(x) = √x. To find the x-intercept, we set f(x) = √x = 0 and solve for x. However, since the square root of a number is always non-negative, there are no values of x between 0 and 1 that make f(x) equal to zero. Therefore, there are no x-intercepts in this range.

For the second part of the function, when x > 1, f(x) = 1/x. To find the x-intercept, we set f(x) = 1/x = 0 and solve for x. However, we cannot divide any number by zero, so there are no x-intercepts in this range either.

Therefore, this function does not have any intercepts.

(b). To graph the function, we need to plot the points on the coordinate plane and connect them.

For the first part of the function, when 0 ≤ x ≤ 1, we have f(x) = √x. The graph of the function will start at the point (0,0) and continuously increase as x increases, approaching (1, 1) as x approaches 1. The graph will be a curve that starts at the origin and reaches (1, 1) at x = 1.

For the second part of the function, when x > 1, we have f(x) = 1/x. The graph of the function will start at (1, 1) and approach the x-axis as x increases. The graph will be a hyperbola opening downwards.

(c). The domain of a function is the set of all possible input values, while the range is the set of all possible output values.

For the first part of the function, when 0 ≤ x ≤ 1, the domain includes all values between 0 and 1, inclusive. Therefore, the domain is [0, 1].

The range of √x is all non-negative real numbers, including zero. Therefore, the range for the first part of the function is [0, ∞).

For the second part of the function, when x > 1, the domain includes all values greater than 1. Therefore, the domain is (1, ∞).

The range of 1/x is all non-zero real numbers. Therefore, the range for the second part of the function is (-∞, 0) U (0, ∞).

Putting it all together, the domain of the function f(x) is [0, 1) U (1, ∞) and the range is [0, ∞) U (-∞, 0) U (0, ∞).