Question

sketch a graph of $f(x)=|x + 2|-2$. before sketching the graph, determine where the function has its minimum or maximum value so you can place your first point there.
the zeros of the function are at the values
the x - intercept(s) are at the points
the y - intercept is at the point

Explanation:

Step1: Find zeros of the function

To find the zeros, set \( f(x) = 0 \), so \( |x + 2| - 2 = 0 \).
Adding 2 to both sides: \( |x + 2| = 2 \).
This gives two cases:
Case 1: \( x + 2 = 2 \), then \( x = 2 - 2 = 0 \).
Case 2: \( x + 2 = -2 \), then \( x = -2 - 2 = -4 \).

Step2: Find x - intercepts

The x - intercepts are the points where \( y = 0 \), which are the same as the zeros. So the x - intercepts are at \( x=-4 \) and \( x = 0 \), so the points are \( (-4,0) \) and \( (0,0) \).

Step3: Find y - intercept

To find the y - intercept, set \( x = 0 \) in \( f(x) \).
\( f(0)=|0 + 2|-2=|2|-2 = 2 - 2=0 \). So the y - intercept is at the point \( (0,0) \).

Answer:

s:

• The zeros of the function are at the values \( x=-4 \) and \( x = 0 \).
• The x - intercept(s) are at the points \( (-4,0) \) and \( (0,0) \).
• The y - intercept is at the point \( (0,0) \).