Question

Wich of the following functions is graphed below??

Answer 1

C. y = |x+4| - 2

Explanation:

Let's split the given graph into two parts, x <-4 and x > -4.

When x = -6, y = 0. When x = -4, y = -2. So the slope of the line is (-2-0)/(-4+6) = -1.

As the line passes through (-6,0), the equation of the straight line is

y - 0 = -1 * (x - (-6) )

=> y = -(x+6) for x <= -4,

or y = -(x+4) - 2. for x+4 <=0 -------(1)

For x >= -4, we can clearly see that the slope of the rising straight line is is +1. It passes through (0,2). So

y - 2 = 1 (x - 0)

y = x + 2, for x >= -4 or

y = (x + 4) - 2 for x+4 >=0 ----------(2)

Thus the equation of the graphed function is

y = |x+4| - 2.

Answer 2

`\textsf{C.} \quad y=|x+4|-2`

Explanation:

The vertex form of an absolute value function is given by:

`\large\boxedf(x)=a`

where:

• a is the coefficient that determines the vertical stretch or compression of the graph. If a is negative, the graph is reflected in the x-axis.
• (h, k) is the vertex.

The given graph shows an absolute function with a positive coefficient "a" and a vertex at (-4, -2). Therefore:

• h = -4
• k = -2

Substitute the values of h and k into the vertex formula:

`y=a|x-(-4)|+(-2)`

`y=a|x+4|-2`

Assuming a = 1, then the function that represents the graphed function is:

`\large\boxedy=`