Answer:
f(x) = l x + 5 l - 1
Blank one: x + 5
Blank two: - 1
Step-by-step explanation:
The graph of an absolute value function forms a V-shape, and is symmetric about the vertical line that passes through its vertex.
If the leading coefficient of the absolute value term is positive, the graph opens upwards. Whereas, if the leading coefficient of the absolute value term is negative, the graph opens downwards.
The general form of an absolute value function is:
\(f(x) = a |x - h| + k\)
where:
- a is the leading coefficient.
- h is the x-coordinate of the vertex.
- k is the y-coordinate of the vertex.
The vertex of an absolute value function is the point where the graph changes direction, forming the "corner" of the V-shape.
The vertex of the graphed function is at (-5, -1). Therefore, h = -5 and k = -1.
Substitute these values into the general equation:
\(f(x) = a|x-(-5)|-1\\\\f(x) = a|x+5|-1\)
To find the value of a, substitute a point on the graph into the function. Let's use point (0, 4):
\(f(0)=4\\\\a|0+5|-1=4\\\\a|5|=4+1\\\\5a=5\\\\a=1\)
The value of a is 1, so:
\(f(x) = 1|x+5|-1\\\\f(x)=|x+5|-1\)
Therefore, the function that is represented by the given graph is:
\(\Large\boxed{\boxed{f(x)=|x+5|-1}}\)
