Question

Select the correct answer. What is the y-intercept of this radical function? \( f(x) = \sqrt[3]{x} - 3 \)?

a. \( (0, -3) \)
b. \( (0, -1) \)
c. \( (0, 0) \)
d. \( (0, 3) \)

Answer 1

The y-intercept of the function f(x) = ∛x - 3 is at the point (0, -3), which occurs where the graph intersects the y-axis when x is zero.

Step-by-step explanation:

To find the y-intercept of the radical function f(x) = ∛x - 3, we need to determine the value of f(x) when x is zero. The y-intercept is the point where the graph of the function crosses the y-axis, which is the line where x equals zero.

So, we substitute x with 0 in the function:

f(0) = ∛(0) - 3 = 0 - 3 = -3.

Therefore, the y-intercept is at the point (0, -3).