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Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.

vesna_86 [32]

Factorize the denominator:

$\dfrac{x^2-4}{x^3+x^2-4x-4}=\dfrac{x^2-4}{x^2(x+1)-4(x+1)}=\dfrac{x^2-4}{(x^2-4)(x+1)}$

If $x\neq\pm2$ , we can cancel the factors of $x^2-4$ , which makes $x=-2$ and $x=2$ removable discontinuities that appear as holes in the plot of $g(x)$ .

We're then left with

$\dfrac1{x+1}$

which is undefined when $x=-1$ , so this is the site of a vertical asymptote.

As $x$ gets arbitrarily large in magnitude, we find

$\displaystyle\lim_{x\to-\infty}g(x)=\lim_{x\to+\infty}g(x)=0$

since the degree of the denominator (3) is greater than the degree of the numerator (2). So $y=0$ is a horizontal asymptote.

Intercepts occur where $g(x)=0$ ( $x$ -intercepts) and the value of $g(x)$ when $x=0$ ( $y$ -intercept). There are no $x$ -intercepts because $\dfrac1{x+1}$ is never 0. On the other hand,

$g(0)=\dfrac{0-4}{0+0-0-4}=1$

so there is one $y$ -intercept at (0, 1).

The domain of $g(x)$ is the set of values that $x$ can take on for which $g(x)$ exists. We've already shown that $x$ can't be -2, 2, or -1, so the domain is the set

$\{x\in\mathbb R\mid x\neq-2,x\neq-1,x\neq2\}$

8 0

3 years ago

If a + 1 = b, then b > a.

kogti [31]

If a=-10;then:
a+1=-10+1=-9=b
-9>-10

if a=10; then
a+1=10+1=11=b
11>10
A)The pair of values for a and be are: a=-10, then the value of b would be: -9;
And a=10; then the value of b would be:11;

B) It isn´t possible to create a pair of values for a and be, in wich the numerical relationship shown in the given conditional stament is false, therefore b>a if a+1=b

4 0

3 years ago

Read 2 more answers

Jim is saving nickels, dimes and quarters to buy a baseball mitt. He has 12 more

Harrizon [31]

Answer:

36 quarters 48 dimes 64 nickels

Step-by-step explanation:

quarter = q

dime = q+12

nickel = 2q-8

$17 = 1,700 cents

(q)25 + (q+12)10 + (2q-8)5 = 1,700

25q +10q+120 +10q-40 =1,700

45q+80 = 1,700

45q = 1620

q= 36

36 QUARTERS x25 = 900cents

48 DIMES x10 = 480 cents

64 NICKELS x 5 = 320 cents

TOTAL 1,700 cents ($17)

5 0

2 years ago

How can you use substitution to solve a system of linear equations?

makvit [3.9K]

Step 1:
Solve one of the equations for either x = or y = .
Step 2:
Substitute the solution from step 1 into the other equation.
Step 3:
Solve this new equation.
Step 4:
Solve for the second variable.

Example 1: Solve the following system by substitution
Substitution Method Example
Solution:
Step 1: Solve one of the equations for either x = or y = . We will solve second equation for y.
solution step 1
Step 2: Substitute the solution from step 1 into the second equation.
solution step 2
Step 3: Solve this new equation.
solution step 3
Step 4: Solve for the second variable
solution step 4
The solution is: (x, y) = (10, -5)
Hope this helps!

6 0

3 years ago

I need help making a proof for geometry! Here is the question…

MatroZZZ [7]

Answer:

Step-by-step explanation:

4 0

2 years ago