Questions: Which function is represented by the graph? f(x)=-2x+1 f(x)=-1/2x+1 f(x)=-2x+1 f(x)=-1/2x+1

Transcript text: Which function is represented by the graph? $f(x)=-2|x|+1$ $f(x)=-\frac{1}{2}|x|+1$ $f(x)=-2|x+1|$ $f(x)=-\frac{1}{2}|x+1|$

Solution

Solution Steps

Step 1: Analyze the graph

The graph is a V-shaped graph, which means it represents an absolute value function. The vertex of the graph is at (0, 1). The graph opens downwards, which means the coefficient of the absolute value term is negative.

Step 2: Determine the slope

The graph passes through the points (0, 1) and (2, -3). The slope of the line segment connecting these two points is $$ \frac{-3 - 1}{2 - 0} = \frac{-4}{2} = -2 $$ Since the graph opens downwards, the slope of the right side of the V is -2. This means the function has the form $ f(x) = -2|x| + c $ for some constant c.

Step 3: Determine the vertical shift

The vertex is at (0, 1), so the graph is shifted up by 1 unit. This means c = 1. So, the function represented by the graph is $ f(x) = -2|x| + 1 $.