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3 years ago

15

How would you "remove the discontinuity" of f? In other words, how would you define f(5) in order to make f continuous at 5? f(x

) = [(x^2 -2x -15)/x-5]

1 answer:

satela [25.4K]3 years ago

4 0

Given f(x) = [(x^2 -2x -15)/x-5], notice it is a rational function

But the numerator x^2 -2x -15 could be factored, which yields

(x – 5)(x + 3)

Therefore f(x) = (x – 5)(x + 3)/ (x-5)

Cancelling x-5, f(x) = x + 3

In this way, the f(x) is continuous at any point, and is basically a line.

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The equation of a linear function in point-slope form is y – y1 = m(x – x1). Harold correctly wrote the equation y = 3(x – 7) us

xz_007 [3.2K]

For this case we must find the point that Harold used to arrive at the following equation:

$y = 3 (x-7)$

Starting from the fact that the equation of the point-slope form of a line is given by:

$(y-y_ {1}) = m (x-x_ {1})$

If we compare the standard equation with Harold's, we see that the slope of the line is $m = 3.$

In addition, it is observed that $x_ {1} = 7$ and $y_ {1} = 0.$

Then, the correct option is: Harold used the point (7,0)

ANswer:

When Harold wrote his equation, the point was used (7,0).

8 0

3 years ago

Read 2 more answers

Convert the rational expression to a radical...don't mind the answers I put I just need someone to show me how they do it step b

bazaltina [42]

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-----------------------------\\\\
thus\implies x^{\frac{2}{5}}\implies \sqrt[5]{x^2}
\\\\\\
and\implies (4ab)^{\frac{3}{5}}\implies \sqrt[5]{(4ab)^3}\implies \sqrt[5]{4^3a^3b^3}
\\\\
-----------------------------\\\\

now\\\\ 4\to 2^2\qquad and\qquad 4^3\to (2^2)^3\to 2^{2\cdot 3}\to 2^6\to 2^{5+1}\to 2^52^1\\\\
-----------------------------\\\\

$

$\bf \sqrt[5]{4^3a^3b^3}\implies \sqrt[5]{2^52^1a^3b^3}\implies 2\sqrt[5]{2a^3b^3}$

8 0

4 years ago

12. Sydney Star bought a new sweatshirt for $42.00. Sales tax was 8%.

levacccp [35]

Answer:

$45.36

Step-by-step explanation:

100 + 8 = 108

42/100 X 108 = 45.36

6 0

3 years ago

Read 2 more answers

Multiply:(xadd1)(xadd2)

erica [24]

3x? I don’t get the question. I think that’s the answer.

8 0

3 years ago

Read 2 more answers

Which function has a range of y < 3?<br> y - 3(2)<br> y = 2(3)<br> O y=-(2)x+ 3<br> Oy- (2) * - 3

defon

Given:

The range of a function is $y$ .

To find:

The function for the given range from the given options.

Solution:

In option A, the given function is:

$y=3(2)^x$

Here, $(2)^x$ is always greater than 0. So, $3(2)^x$ is also greater than 0, i.e., $y>0$ .

In option B, the given function is:

$y=2(3)^x$

Here, $(3)^x$ is always greater than 0. So, $2(3)^x$ is also greater than 0, i.e., $y>0$ .

In option C, the given function is:

$y=-(2)^x+3$

Here,

$(2)^x>0$

$-(2)^x$

$-(2)^x+3$

$y$

The range of this function is $y$ . So, option C is correct.

In option D, the given function is:

$y=(2)^x-3$

Here,

$(2)^x>0$

$(2)^x-3$

$y$

The range of this function is $y$

Therefore, the correct option is only C.

6 0

3 years ago