9514 1404 393
Answer:
y = 28(x +5)(x -2)/((x +5)(x +7)(x -8))
Step-by-step explanation:
The vertical asymptotes at x=-7 and x=8 and the hole at x=-5 tell you that the denominator has factors of (x +7)(x +5)(x -8) and the numerator has a factor of (x +5). The zero-crossing at x=2 tells you there is another numerator factor of (x -2). So, for some vertical scale factor 'a', the function so far must be ...
f(x) = a(x +5)(x -2)/((x +7)(x +5)(x -8))
For this, we have ...
f(0) = 10a/280 = a/28
We want f(0) = 1, so the value of 'a' must be 28.
The equation that produces the graph is ...
y = 28(x +5)(x -2)/((x +5)(x +7)(x -8))
