Question

Let f(x) = |x-21-4. Sketch f(x) for x>0 and label where f crosses the z-axis

Answer 1

To sketch the graph of the function f(x) = |x-21-4| for x>0, we consider two cases: when x-21-4>0 and when x-21-4<0. The graph crosses the z-axis at x = 25.

Step-by-step explanation:

To sketch the graph of the function f(x) = |x-21-4| for x>0, we need to understand the absolute value function. The absolute value of a number is its distance from zero on the number line. In this case, the function |x-21-4| represents the absolute value of (x-21-4). So, when x-21-4>0, the function is equal to (x-21-4), and when x-21-4<0, the function is equal to -(x-21-4).

Now, let's consider the two cases:

1. If x-21-4>0, then f(x) = (x-21-4). For x>0, this means that f(x) = x-25.
2. If x-21-4<0, then f(x) = -(x-21-4). For x>0, this means that f(x) = -(x-25).

When f(x) crosses the z-axis, it means that the value of f(x) is equal to 0. So, we need to solve the equation f(x) = 0 for both cases:

1. For f(x) = x-25, when x-25 = 0, x = 25.
2. For f(x) = -(x-25), when -(x-25) = 0, x = 25.

Therefore, the graph of f(x) crosses the z-axis at x = 25.