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Mademuasel [1]
3 years ago
15

Two functions are shown below.

Mathematics
1 answer:
frozen [14]3 years ago
5 0

Answer:

x = 6

Step-by-step explanation:

As the function f(x) is an exponencial function, it will grow faster than g(x), that is a linear function.

For small values of x, we have that f(x) < g(x). For example:

f(1) = 1/2 * 2 = 1

g(1) = 5*1 + 2 = 7

f(2) = 1/2 * 4 = 2

g(2) = 5*2 + 4 = 14

So we just need to check some integer values and see when f(x) will be bigger than g(x). It will not be a big value, as the exponencial function grows very fast.

For x = 5, we have:

f(5) = 1/2 * 32 = 16

g(5) = 5*5 + 4 = 29

For x = 6, we have:

f(6) = 1/2 * 64 = 32

g(6) = 5*6 + 4 = 34

For x = 7, we have:

f(7) = 1/2 * 128 = 64

g(7) = 5*7 + 4 = 39

So the largest integer value of x for f(x) ≤ g(x) is x = 6.

Another way to solve this is by plotting both equations, and then checking where they cross, that is, where f(x) = g(x).

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Give an example of a rational function that has a horizontal asymptote at y = 1 and a vertical asymptote at x = 4.
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Answer:

Possibility 1: \frac{(x+1)(x+1)}{(x-4)(x+5)}

Possibility 2: \frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}

Possibility 3: \frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}

There are infinitely many more possibilities.

Step-by-step explanation:

So we are looking for a fraction in terms of x.

We have a horizontal asymptote so that means the degree of the top has to equal to degree of the bottom. It is also at y=1 which means the coefficient of the leading term on top and bottom must be the same (but not zero) since the same number divided by the same number is 1.  

Now we also have a vertical asymptote at x=4 which means we need a factor of x-4 on bottom.

So there is a lot of possibilities. Here are a few:

Possibility 1: \frac{(x+1)(x+1)}{(x-4)(x+5)}

You have the degrees are the same on top and bottom and the leading coefficients are the same.  You also have that factor of (x-4) on bottom.

Possibility 2: \frac{(x+1)(x+3)(x-3)}{x(x-4)(x+5)}

Possibility 3: \frac{-4(x-4)(x+1)}{-4(x-4)(x-4)}

Now a factor of (x-4) can be canceled here but you still have a factor of (x-4) left on bottom so you still have the vertical asymptote. You also still have the same leading coefficient on top and bottom (-4 in this case) and the same degree.

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Need help with this problem
Lera25 [3.4K]

The employee receives $162 because you just substitute 6 for h and w for 3 which is 12(6)+30(3) and 12x6=72 and 30x3=90 and 72+90=162

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