Identify the holes, vertical asymptotes and horizontal asymptotes of f(x)=x²+7x+12/-x²-3x+4
1 answer:
<h3>Answer:</h3>
- hole: x = -4
- vertical asymptote: x = 1
- horizontal asymptote: y = -1
The function factors as ...
... f(x) = -(x+3)(x+4)/((x-1)(x+4)) = -(x+3)/(x-1) . . . . x ≠ -4
and the quotient is ...
... f(x) = -(1 +4/(x-1))
... f(x) = -1 -4/(x-1) . . . . . x ≠ -4
This has a hole at x = -4 (where the denominator factor cancels the numerator factor), a vertical asymptote at x=1 (where the denominator is zero), and a horizontal asymptote at y = -1 (the value of the function for large values of x).
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Answer:
The equation in the slope-intercept form will be:
y = 1/4x - 7
Step-by-step explanation:
Given the points
- (-4.-8)
- (-8, -9)
We know that the slope-intercept of line equation is
where m is the slope and b is the y-intercept
substituting m = 1/4 and the point (-4, -8) to find the y-intercept 'b'
y = mx+b
-8 = 1/4(-4)+b
-8 = -1 + b
b = -8+1
b = -7
so the y-intercept = b = -7
substituting m = 1/4 and b = -7 in the slope-intercept form of line equation
y = mx+b
y = 1/4x + (-7)
y = 1/4x - 7
Thus, the the equation in slope-intercept form will be:
y = 1/4x - 7