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3 years ago

Which of these statements is true for f(x)=3•(9)^x

Mathematics

2 answers:

svlad2 [7]3 years ago

8 0

A. The y-intercept is (0,3)

max2010maxim [7]3 years ago

4 0

Answer:

Option A is the correct choice.

Step-by-step explanation:

We have been given an equation $f(x)=3\cdot (9)^x$ . We are asked to choose the correct statement about our given equation.

Let us see our given choices one by one.

A. The y-intercept is (0,3).

Let us find the y-intercept by substituting $x=0$ in our given equation.

$f(0)=3\cdot (9)^0$

$f(0)=3\cdot 1$

$f(0)=3$

Since the y-intercept of our given equation is (0,3), therefore, option A is the correct choice.

B. It is always decreasing.

We can see from our given equation that our given function represents exponential growth, where growth factor is 9, therefore, option B is not correct.

C. The domain of $f(x)$ is $x>0$ .

Since our function is defined for all real values of x, therefore, the domain of function is $(-\infty,\infty)$ and our given statement is not true.

D. The y-intercept is (0,1).

Since the y-intercept of our given equation is (0,3), therefore, option D is not a correct choice.

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Points (−6, 3) and (−6, −3) on the coordinate grid below show the positions of two dogs at a park: A coordinate plane is shown.

Nostrana [21]

Question:

Points (−6, 3) and (−6, −3) on the coordinate grid below show the positions of two dogs at a park.There is a point at (−6, 3) labeled Dog 1. There is a point at (−6, −3) labeled Dog 2.

Which statement best describes the relationship between the positions of the two players?

A.Dog 1's position is Dog 2's position reflected across the y-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.

B.Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.

C.Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the x-coordinates of Dog 1 and Dog 2 are different.

D. Dog 1's position is Dog 2's position reflected across the y-axis; only the signs of the x-coordinates of Dog 1 and Dog 2 are different.

Answer:

Option B: Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.

Explanation:

The position of the Dog 1 is (−6, 3).

The position of the Dog 2 is (−6, -3).

From the graph, we can see that the image of Dog 1 is reflected over x-axis. Because to reflect an image over x-axis, the signs of y-coordinate must be changed.

Hence, Option B is correct.

Thus, Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.