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4 years ago

What transformation is represented by the rule (x, y)→(y, − x) ?

Mathematics

2 answers:

Svetllana [295]4 years ago

8 0

A refection on the y=x line and x=-x

11111nata11111 [884]4 years ago

4 0

Answer:

The answer is reflection around an X axis.

Step-by-step explanation:

In order to determine the answer, we have to know about reflection procedure.

A reflection procedure is when any figure, line or point is drawing again with different coordinates, but maintaining the geometry. It is the same effect that is produced by a mirror.

The reflection happens around an axis. The condition (x,y)→(y, − x) happens when we use the X-axis.

Finally, the transformation is represented by a reflection around an X axis.

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Fred borrows $40 at 0.8% simple interest per month. When Fred pays the loan back 2 years later, how much interest does Fred pay?

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3 years ago

Show all worked identify the asymptotes and state the end behavior of the function F(x)=6x over x-36

astraxan [27]

Solution

Asymptote:

Vertical Asymptote

- The vertical asymptotes of a rational function are determined by the denominator expression.

- The expression given is:

$f(x)=\frac{6x}{x-36}$

- The denominator of (x- 36) determines the asymptote line.

- The vertical asymptote defines where the rational function isundefined. Iin order for a rational function to be undefined, its denominator must be zero.

- Thus, we can say:

$\begin{gathered} x-36=0 \\ Add\text{ 36 to both sides} \\ \\ \therefore x=36 \end{gathered}$

- Thus, the vertical asymptote is

$x=36$

Horizontal Asymptote:

- The horizontal asymptote exists in two cases:

1. When the highest degree of the numerator is less han the degree of the demnominator. In this case, the horizontal asymptote is y = 0

2. When the highest degee sof the numerator and tdenominator are the same. In this case, the horizontal asymptote is

$\begin{gathered} y=\frac{N}{D} \\ where, \\ N=\text{ Coefficient of the highest degree of the numerator} \\ D=\text{ Coefficient of the highest degree of the denominator} \end{gathered}$

- For our question, we can see that the highest degrees of the numerator and denominator are the same. Thus, we have the Horizontal Asymptote to be:

$y=\frac{6}{1}=6$

End behavior:

- The end behavior is examining the y-values of the function as x tendsto negative and positive infinity.

- Thus, we have that:

$\begin{gathered} f(x)=\frac{6x}{x-36} \\ \\ \text{ Divide top and bottom by }x \\ f(x)=\frac{6x}{x-36}\times\frac{x}{x} \\ \\ f(x)=\frac{\frac{6x}{x}}{\frac{x-36}{x}}=\frac{6}{1-\frac{36}{x}} \\ \\ As\text{ }x\to-\infty \\ f(-\infty)=\frac{6}{1-\frac{36}{-\infty}}=\frac{6}{1+\frac{36}{\infty}}=\frac{6}{1+0}=6 \\ \\ \text{ Thus, we can say: }x\to-\infty,f(x)\to6 \\ \\ Also, \\ As\text{ }x\to\infty \\ f(\infty)=\frac{6}{1-\frac{36}{\infty}}=\frac{6}{1-0}=6 \\ \\ \text{ Thus, we can also say: }x\to\infty,f(x)\to6 \end{gathered}$

Final Answers

Asymptotes:

$\begin{gathered} \text{ Vertical:} \\ x=36 \\ \\ \text{ Horizontal:} \\ y=6 \end{gathered}$

End behavior:

$\begin{gathered} As\text{ }x\to-\infty,f(x)\to6 \\ \\ As\text{ }x\to\infty,f(x)\to6 \end{gathered}$

7 0

1 year ago

Solve 2x - 71 > 11

3241004551 [841]

Answer:

x>41

Step-by-step explanation:

Add 71 to both sides, then divide by 2.

I hope this helps :)

8 0

3 years ago