The equation of the graphed absolute value function is y ≤ -1 | x - 3| + 4
How to write absolute value function graph
Absolute value function graph is written using the formula
y = a | x − h | + k
where the vertex has coordinates (h, k)
From the graph
h = 3
k = 4
Plugging in the values to the equation
y = a | x − h | + k
y = a | x − 3 | + 4
Using point (0, 1) from the graph, we solve for a
1 = a |0 − 3 | + 4
1 - 4 = a |0 − 3 |
-3 = a |-3 |
-3 = 3a
a = -1
Hence the equation is
y = -1 | x - 3| + 4
considering the inequality, we have (for shading below the line)
y ≤ -1 | x - 3| + 4