The graph of the linear function f is shown in the xy-plane above. The graph of the linear function g (not shown) is perpendicular to the graph of f and passes through the point (1,3). What is the value of g(0) ?

Answer

2.5

Explanation

The graph of the linear function f passes through the points (0, 3) and (1, 1). The slope of the graph of the function f is therefore `(1-3)/(1-0)`=-2. It’s given that the graph of the linear function g is perpendicular to the graph of the function f. Therefore, the slope of the graph of the function g is the negative reciprocal of −2, which is `− 1/(-2)=1/2`, and an equation that defines the function g is `g(x)=1/2x+b`, where b is a constant. Since it’s given that the graph of the function g passes through the point (1, 3), the value of b can be found using the equation `3=1/2(1)+b`. Solving this equation for b yields `b=5/2`. so an equation that defines the function g is g(x)=`1/2x+5/2`. F inding the value of g(0) by substituting 0 for x into this equation yields `g(0) =1/2(0)+5/2` or `5/2` . Either 2.5 or 5/2 may be entered as the correct answer.