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2 years ago

9

How do you find the domain of a linear grap

2 answers:

Shalnov [3]2 years ago

6 0

Finding the domain of a function from its rule is not difficult. Look at the examples below carefully.

1) Give the domain of each.

a) f(x) = 3/(x - 5) The domain consists of all numbers for x that are defined for the function. Since the function doesn't exist at x = 5 ( it makes the denominator 0), the domain is all real numbers but 5.

b) f(x) = Since 4 - x is under the radical, 4 - x must be greater than or equal to zero, otherwise the answers will be imaginary. To find the domain, solve the inequality 4 - x > 0.
-x > -4
x < 4. Thus, all numbers less than or equal to 4 represent the domain for this function.

IceJOKER [234]2 years ago

4 0

The domain is all possible x values. For linear graphs, the domain is usually all real numbers.

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3 years ago

Simplify the expression state any excluded values<br> 2a^2-4a+2<br> ---------------<br> 3a^2-3

chubhunter [2.5K]

Answer:

The simplified form is $\dfrac{2(x-1)}{3(x+1)}$ .

$x =1$ is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

$\dfrac{2a^2-4a+2}{3a^2-3}$

Let us simplify the numerator and denominator separately.

The numerator is given as $2a^2-4a+2$

2 is a common factor in all the three terms. So, we factor it out. This gives,

$=2(a^2-2a+1)$

Now, $a^2-2a+1=(a-1)(a-1)$

Therefore, the numerator becomes $2(a-1)(a-1)$

The denominator is given as: $3a^2-3$

Factoring out 3, we get

$3(a^2-1)$

Now, $a^2-1$ is of the form $a^2-b^2=(a-b)(a+b)$

So, $a^2-1=(a-1)(a+1)$

Therefore, the denominator becomes $3(a-1)(a+1)$

Now, the given expression is simplified to:

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

There is $(x-1)$ in the numerator and denominator. We can cancel them only if $x\ne1$ as for $x=1$ , the given expression is undefined.

Now, cancelling the like terms considering $x\ne1$ , we get:

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

Therefore, the simplified form is $\dfrac{2(x-1)}{3(x+1)}$

The simplification is true only if $x\ne1$ . So, $x =1$ is the excluded value for the given expression.

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3 years ago

5a + 5b + 5c = −20 <br> 4a + 3b + 3c = −6 <br> −4a + 3b + 3c = 9

PolarNik [594]

Answer:

Step-by-step explanation:

7 0

3 years ago

What is the common ratio between successive terms in a sequence?<br> 1.5, 1.2,0.96, 0.768, ...

Vanyuwa [196]

9514 1404 393

Answer:

0.8

Step-by-step explanation:

The ratio of the first two terms is ...

1.2/1.5 = 4/5 = 0.8

That is also the ratio of successive adjacent terms.

0.96/1.2 = 0.768/0.96 = 0.8

The common ratio is 0.8.

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3 years ago

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Phantasy [73]

Answer:

.................................

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3 years ago