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3 years ago

For which interval is the function constant?

Mathematics

1 answer:

andreev551 [17]3 years ago

4 0

Answer:

Option D (2, 6)

Step-by-step explanation:

As shown in the graph function has four intervals on which graph is plotted.

1). From the graph we can see in the interval -10 ≤ x ≤ 0 graph is increasing.

2). From 0 ≤ x ≤ 2 function is decreasing.

3). Between 2 ≤ x ≤ 6 function is constant.

4). And for x ≥ 6 function is increasing.

Therefore interval in which the function is constant is (2, 6).

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On a coordinate plane, 2 exponential fuctions are shown. Function f (x) decreases from quadrant 2 into quadrant 1 and approaches

Gala2k [10]

Answer:

$g(x)=6(3)^x$

Step-by-step explanation:

We are given that

$f(x)=6(\frac{1}{3})^x$

Function f decreases from quadrant 2 to quadrant 1 and approaches y=0

It cut the y- axis at (0,6) and passing through the point (1,2).

Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.

It passing through the point (-1,2) and cut the y-axis at point (0,6).

Reflection across y- axis:

Rule of transformation is given by

$(x,y)\rightarrow (-x,y)$

Using the rule then we get

$g(x)=6(\frac{1}{3})^{-x}=6(3)^x$

By using

$x^{-a}=\frac{1}{x^a}$

Substitute x=-1

$g(-1)=6\times (\frac{1}{3})=2$

Substitute x=0

$g(0)=6$

Therefore, $g(x)=6(3)^x$ is true.

8 0

2 years ago

Read 2 more answers

The sum of two consecutive natural numbers is 525.<br> Find the numbers.

Luda [366]

Answer:

262 and 263 are consecutive natural numbers whose sum is 525.

Step-by-step explanation:

Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. ( $|x-y| = 1$ , $\forall\,x,y \in \mathbb{N}$ ) We can interpret the statement mathematically by means of the following expression: