Question

Identify the x-intercept(s) and vertex of the function y=1−1/3|x+3|
The function has x-intercepts at---------- while it has a vertex at--------------
(6, 0) and (0, 0)
(-6, 0) and (0, 0)
(3, 1) .
(3, -1) .
(-3, 1) .
(-3, -1) .

Answer 1

The x-intercepts are the points where the graph of the function crosses the x-axis. At these points, the y-coordinate is equal to 0.

To find the x-intercepts, we can set y = 0 and solve for x:

0 = 1 - 1/3|x + 3|

Since the absolute value of any number is always nonnegative, the expression |x + 3| is equal to 0 only when x + 3 = 0. Therefore, the x-intercept is at x = -3.

So, the function has an x-intercept at (-3, 0).

Now let's find the vertex of the function. The vertex of the absolute value function y = |x| is always at (0, 0). However, when we add or subtract numbers inside the absolute value function, it shifts the graph horizontally. In this case, we are subtracting 3, so the vertex will shift 3 units to the left.

Therefore, the vertex of the function y = 1 - 1/3|x + 3| is at (-3, 0).

So, the correct answer is (-3, 0) and (0, 0).