All categories

2 years ago

state the domain, the range, and the intervals on which function is increasing, decreasing, or constant in interval notation

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

8 0

Answer:

domain (-∞, ∞)
range (-∞, 4]
increasing (-∞, 0)
decreasing (0, ∞)
constant (only at x=0, not on any interval)

Step-by-step explanation:

The graph is of the equation y = -x^2 +4. It is a polynomial of even degree, so has a domain of all real numbers: (-∞, ∞).

The vertical extent of the graph includes y=4 and all numbers less than that:

range: (-∞, 4]

The graph is increasing to the left of its vertex at x=0, decreasing to the right.

increasing (-∞, 0); decreasing (0, ∞)

There is no interval on which the function is constant. It has a horizontal tangent at x=0, but a single point does not constitute an interval.

You might be interested in

Sal knows the volume of a cylinder is 500 cubic units. He wants to create a cylinder with twice the volume. Which variation of t

kherson [118]

You can double the height

8 0

2 years ago

An economist believes that interest rates for thirty-year fixed-rate mortgage loans are decreasing. To investigate this further,

Contact [7]

Answer:

The null hypothesis is $H_0: p = 0.22$

The alternate hypothesis is $H_1: p < 0.22$

Step-by-step explanation:

To investigate this further, the economist would like to test the claim that the percent of thirty-year fixed-rate mortgage loans that have a 4.75 percent interest rate is less than 22%.

At the null hypothesis, we test that the proportion is of 22%, that is:

$H_0: p = 0.22$

At the alternate hypothesis, we test that the proportion is less than 22%, that is:

$H_1: p < 0.22$

7 0

2 years ago

A researcher claims that a post-lunch nap decreases the amount of time it takes to run 20 meters. Ten subjects are randomly sele

MakcuM [25]

Answer:

4. A post-lunch nap decreases the amount of time it takes males to sprint 20 meters.

Step-by-step explanation:

This question wants us to state the claim and the hypothesis.

This researchers claim can be found in the first sentence of this question.

Claim: post lunch nap decreases the time it takes to run for 20 meters.

The correct answer option for the claim is the 4th answer option. And it means that sleeping after lunch reduces the time it takes males to run in a 20m race.

B. Hypothesis

H0: Ud <= 0

H1: Ud > 0

d = is the race time without a nap - race time with a nap

5 0

2 years ago

Am I correct?? I did not count the last square unit at the vertices of each corner.

mariarad [96]

The answer would actually be a 110 units because the bottom left corner had 20 units and the bigger square had 90.

3 0

2 years ago

When Θ = 5 pi over 6, what are the reference angle and the sign values for sine, cosine, and tangent? Θ' = negative pi over 6; s

timama [110]

Answer:

Option C is correct.

Step-by-step explanation:

$\theta=\frac{5\pi }{6}$

We need to find reference angle and signs of sinФ, cosФ and tanФ

We know that $\theta=\frac{5\pi }{6}radians$ is equal to 150°

and 150° is in 2nd quadrant.

So, Ф is in 2nd quadrant.

And In 2nd quadrant sine is positive, while cos and tan are negative

The reference angle Ф' is found by: π - Ф

=> Ф = 5π/6

so, Reference angle Ф' = π - 5π/6

Ф' = 6π - 5π/6

Ф' = π/6

So, Option C Θ' = pi over 6; sine is positive, cosine and tangent are negative is correct.

5 0

3 years ago