CPM Homework Help : PC3 Problem 7-54

The graphs of $y=f(x)$ , $y=g(x)$ , and $y=h(x)$ , are shown below. Far below are the graphs of the reciprocal of two of the functions from above. Express $a(x)$ and $b(x)$ in terms of one of the functions listed above.

Downward parabola labeled, f of x, vertex at the point (1, comma 4), passing through the points (negative 1, comma 0), & (3, comma 0). Continuous curve labeled, g of x, starting in lower left, turning at the point (negative 3, comma 3), at the point (1.5, comma negative 5), continuing up & right, with intercepts at (negative 4, comma 0), (0, comma negative 3), & (3, comma 0). Continuous curve labeled, h of x, starting in upper left, turning at the point (negative 2, comma negative 5.5), at the point (2.5, comma 2), continuing down & right, with intercepts at (negative 4, comma 0), (0, comma negative 2.5), (1, comma 0) & (4, comma 0).

Hint:

When $f(x)=0$ , then $\frac{1}{f\left(x\right)}$ is undefined, creating a vertical asymptote.

Sketch the reciprocal of the function that was not used in parts (a) or (b).