# pre cal

f(x) = two divided by quantity x squared minus two x minus three

Graph

A coordinate axis scaled by one.

Domain and Range : _____________________

x and y Intercept(s) : _____________________

Horizontal Asymptote(s) : ___________________

Vertical Asymptote(s) : ____________________

f(x) = quantity x squared plus x minus two divided by quantity x squared minus three x minus four

Graph
A coordinate axis scaled by one.

Domain and Range : _____________________

x and y Intercept(s) : _____________________

Horizontal Asymptote(s) : ___________________

Vertical Asymptote(s): ___________________

1. 👍
2. 👎
3. 👁
1. Good grief. How about some math, instead of the noisy words? I'll do one.

f(x) = (x^2+x-2)/(x^2-3x-4)

All polynomials have domain of all reals.
Rationals have a domain of all reals except where the denominator is zero. Since

f(x) = (x+2)(x-1) / (x-4)(x+1)

The domain is all reals except x = -1 or 4

x-intercepts (where y=0) are at -2 and 1
y-intercept (where x=0) is at 1/2

Vertical asymptotes are where the denominator is zero and the numerator is not: x = -1 and 4. Note that those are where f(x) is not defined.

Horizontal asymptotes are where x is very large. In that case, f(x) is approximately

(x^2)/(x^2) = 1

Note that it is possible for the graph to cross the horizontal asymptotes, but at the extreme ends of the x-axis, the curve approaches them.

1. 👍
2. 👎
2. 1. F(x) = 2/(x^2-2x-3)
C = -3 = 1*(-3). 1+(-3) = -2 = B.
F(x) = 2/(x+1)(x-3)

x+1 = 0
X = -1, Denominator = 0.

x-3 = 0
X = 3, Denominator = 0.

Domain = All real values of x except -1,
and 3.

Y-int. = 2/(0+1)(0-3) = 2/-3 = -2/3

No x-intercept, because the numerator is
constant and the fraction cannot be set
to 0.

2. F(x) = (x^2+x-2)/(x^2-3x-4)=
(x-1)(x+2)/(x+1)(x-4).
x+1 = 0
X = -1, Denominator = 0.

x-4 = 0
X = 4, Denominator = 0.

Domain = All real numbers except -1 and
4.

Y-int. = (0-1)(0+2)/(0+1)(0-4) = -2/-4 =
1/2.

Y = (x-1)(x+2)/(x+1)(x-4) = 0
(x-1)(x+2) = 0

x-1 = 0
X = 1 = x-int.

x+2 = 0
X = -2 = x-int.

X-Intercepts = 1, and -2.

1. 👍
2. 👎
3. Thanks!

1. 👍
2. 👎

## Similar Questions

1. ### Math

What is the simplified form of The quantity x to the fourth power minus 81 divided by the quantity x plus 3 ? A. x cubed minus 3 times x squared plus 9 times x minus 27 B. the quantity x squared plus 9 times the quantity x squared

2. ### Calculus AB

Which of the following functions is continuous at x = 3? (5 points) Select one: a. f of x equals the quotient of the quantity x squared minus 9 and the quantity x plus 3 b. f of x equals the quotient of the quantity x squared

3. ### Calculus

PLEASE HELP ME! What is the x-coordinate where the graph of the function represented by the Maclaurin series 1 minus 2 times x plus 4 times x squared over 2 factorial minus 8 times x cubed over 3 factorial plus dot, dot, dot,

4. ### calculus

1.Solve the differential equation dy/dx= y^2/x^3 for y=f(x) with the condition y(1) = 1. 2.Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared. Explain why

1. ### Calculus

Use geometry to evaluate the integral from negative 3 to 3 of f of x, dx for f of x equals the square root of the quantity 4 minus the square of the quantity x plus 1 for x is between negative 3 and 1 including negative 3 and 1,

2. ### Calculus

Match each series to the test that should be used to test for convergence/divergence. While it is possible that each test could apply to more than one series, in this exercise each is only used once. (4 points) 1. the summation

3. ### math

Use geometry to evaluate the integral from negative 4 to 4 of the square root of the quantity 16 minus x squared, dx. pi divided by 4 4π 8π 16π

4. ### Calculus

Let F of x equals the integral from 1 to 3 times x of the natural logarithm of t squared. Use your calculator to find F″(1). A. 12 B. 6 C. 4 D. 1/9 Find the range of the function f of x equals the integral from 0 to x of the

1. ### Math

The area of a rectangular art studio is given by the trinomial 12 x squared plus 5 x minus 2. What are the possible dimensions of the studio? Use factoring. A. left parenthesis 4 x plus 1 right parenthesis and left parenthesis 3 x

2. ### Math

The area of a rectangular room is given by the trinomial x squared plus 3 x minus 28. What are the possible dimensions of the rectangle? Use factoring. A. left parenthesis x minus 7 right parenthesis and left parenthesis x plus 4

3. ### Algebra

Solve the given polynomial equation. Use the Rational Zero Theorem and​ Descartes's Rule of Signs as an aid in obtaining the first root. 2 x cubed minus 5 x squared minus 5 x minus 1 equals 02x3−5x2−5x−1=0

4. ### Calculus

Which of the following integrals cannot be evaluated using a simple substitution? the integral of 1 divided by the quantity x squared plus 1, dx the integral of 1 divided by the quantity x squared plus 1, dx the integral of x