Question

F(x)=∣3x+6∣−1

What is meant by Modulus function?
Determine the following:
The vertex of f(x)
The y-intercept(s) of f(x)

Answer 1

The modulus function represents the absolute value, which outputs non-negative values. For f(x) = |3x + 6| - 1, the vertex is at (-2, 5) and the y-intercept is also at (0, 5).

Step-by-step explanation:

The function f(x) = |3x + 6| - 1 includes a modulus, which in mathematical terms refers to the absolute value function. The modulus function outputs the non-negative value of its input, regardless of whether the input itself is positive or negative. For the function f(x), the modulus part is |3x + 6|, which means that the graph of 3x + 6 is reflected above the x-axis for values of x that would make 3x + 6 negative.

To find the vertex of f(x), we look for the point where 3x + 6 = 0, which occurs when x = -2. Substituting this into the function gives us f(-2) = |-6| - 1 = 5, making the vertex of the graph (-2, 5). The y-intercept occurs where x = 0. Substituting 0 into f(x) gives us f(0) = |0+6| - 1 = 5, which means that the y-intercept is also (0, 5).