# The graph #y=(x^2+5x+7)/(x+2)# is shown below. Find the value of the product #abcd#?

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The dashed vertical line through D (d,0) is a vertical asymptote. The dashed line BC is a slant asymptote. The coordinates of B and C are B(0,b) and C(c,0). The curve crosses the y-axis at A(0,a).

The dashed vertical line through D (d,0) is a vertical asymptote. The dashed line BC is a slant asymptote. The coordinates of B and C are B(0,b) and C(c,0). The curve crosses the y-axis at A(0,a).

##### 1 Answer

#### Explanation:

The question asks us to find various properties of the curve and combine them.

**1) Vertical asymptote, #d#**

Find the vertical asymptote by setting the denominator to 0:

Check that the numerator is not also 0 at the same point:

So this point is not a function hole.

**2) Curve y-intercept, #a#**

We seek the function value

**3) Slant intercept**

Use polynomial long division to express

Divide leading terms:

Repeat:

So

We know from this that the slant asymptote line is

**4) Slant intercept #x#- and #y#-intercepts, #c# and #b#**

For the

For the

**5) Combine results**

From above,

So