Which statements are true regarding f(x)=10/x+5

? Check all that apply.

The domain of f(x) is (–∞, –5) U (–5, ∞).
The range of f(x) is (–∞, 2) U (2, ∞).
The x-intercept is at (–5, 0).
The y-intercept is (0, 2).
There is a vertical asymptote at x = –5.
The end behavior is x → –∞, f(x) → 0 and x → ∞, f(x) → 0.

An asymptote is a straight line that can be horizontal, vertical or oblique that goes closer and closer to a curve which is the graphic of a given function.

What is intercept?

An intercept of any function is a point where the graph of the function crosses, or intercepts, the x-axis or y-axis.
To find the x-intercept we need to do y = 0
To find the y-intercept, we need to do x = 0

How to know the domain of function?

The given function is [tex]\frac{10}{x + 5}[/tex]

Now, if x = -5 then the function becomes undefined.

∴ The domain of the function is all real numbers except -5

So, The domain of f(x) is (–∞, –5) U (–5, ∞).

So, option a is correct.

How to know the range of the function?

Clearly, the range of the function includes all real numbers

So, option B is wrong

How to find the x-intercept?

To find the x-intercept , we will have to solve f(x) = 0, which is not at all possible for this function.

So, option C is wrong

How to find the y-intercept?

To find the y-intercept, we need to do x = 0

So, putting x = 0 in the function we get f(x) = 2

So, the y- intercept is (0, 2).

So, option D is correct.

How to find vertical asymptote ?

To find the vertical asymptote, we need to make the denominator = 0

∴ x+ 5 = 0

∴ x = -5

So, there is a vertical asymptote at x = –5.

Hence option E is correct.

How to find the end behavior?

We can see,

As x tends to -∞, x + 5 will also tend to -∞

We know that a number divided by ∞ or -∞ becomes 0

So, as x tends to -∞, f(x) will tend to 0

So, Option F is correct.

Find more about "Domain and Range of Functions" here: https://brainly.com/question/1942755

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