MA 15800 Exam 2 Qs

Find the coordinates of the y-intercept of the graph of f(x) = 2x^2−14x+20/x^2+8x−20.

(0,−1)

For the following function, find its inverse f^−1(x). f(x)=x^2+1, x≥0

f^−1(x)=√x-1

Find the zero(s) of the function f(x)=x/x^2+5x.

There are no zeros. (0 ⍯ 1)

Select the true statement regarding the function f(x) = x^3+3x^2−4x/x^2+x−12.

There is one vertical asymptote, one hole and one slant asymptote.

Find an equation for a rational function with the following properties: A. Vertical asymptotes at x = 0 and x = 1 B. Horizontal asymptote is y = 0 C. No zeros D. One hole at x = 8

f(x) = x−8/x(x−1)(x−8)

Find an equation for a polynomial of degree 3 with the following properties: 1. zeros at x = −3 and x = 5 2. f(1) = 2 3. f(x) < 0 only on (−∞,−3)

f(x)=1/32(x+3)(x−5)^2

Find the equation of the horizontal asymptote of the function f(x)=1/x^3+5.

y = 0

Find the equation of the slant asymptote of f(x) = x^2+3x−4/x+1

y = x+2

Determine the standard form (y=a(x−h)^2+k) of the equation y = x^2+4x+10.

y=(x+2)^2+6

Find and simplify the difference quotient f(x+h)−f(x)/h for the function f(x)=7/x.

−7/x(x+h)

Find the coordinates of the vertex of f(x)=3x^2+6x−24 and determine whether it occurs at a maximum or a minimum function value.

(−1,−27); minimum (factor a before completing the square; a>0)

What is the domain of the following function? f(x)= x + 9 if x<3 x if 3≤x<7 x^2 + 3 if x>7

(−∞,7) U (7,∞)

What is the domain of the function f(x)=x^2+3x−28?

(−∞,∞)

The growth rate R of a certain species of bird is given by R = (−w^2/4)+w, where w is measured in ounces and R is measured in ounces/year. At what weight is the bird growing at the maximum rate?

2 ounces: (-b/2a; MAXIMUM rate = vertex of parabola)

Given the function f(x)= x if −10 < x ≤ 0 7 if 0 < x < 2 4x + 2 if 2 ≤ x < 5 find f(0)+f(1).

7