seguitzla

2022-10-08

How do you find the range of the function y=f(x)=x^{2}-25 on the domain $-2\le x\le 3$?

aveanoon

Beginner2022-10-09Added 8 answers

The range is the collection of all function outputs that result from a given domain of inputs. In this case, if collect all the results of f(-2), f(3) and all the values of x in between, we've collected the range.

Remember from the graph of ${x}^{2}$ that it has a minimum at x=0 and increases as you increase or decrease x from there. The same is the case with ${x}^{2}-25$. The minimal value it can take is -25, which it takes precisely when x=0. Zero is in our given domain, so we know that the minimum value of the range is -25.

To find the maximum, it suffices to plug in the endpoints, since we know f(x) is increasing as we get more distant from x=0. We have f(-2)=4-25=-21 and f(3)=9-25=-16. The greater value occurs at f(3)=-16.

Since our minimum output is -25 and our maximum is -16, and we hit every value in between, our range is [-25, -16].

Remember from the graph of ${x}^{2}$ that it has a minimum at x=0 and increases as you increase or decrease x from there. The same is the case with ${x}^{2}-25$. The minimal value it can take is -25, which it takes precisely when x=0. Zero is in our given domain, so we know that the minimum value of the range is -25.

To find the maximum, it suffices to plug in the endpoints, since we know f(x) is increasing as we get more distant from x=0. We have f(-2)=4-25=-21 and f(3)=9-25=-16. The greater value occurs at f(3)=-16.

Since our minimum output is -25 and our maximum is -16, and we hit every value in between, our range is [-25, -16].

What is the range of the function $y={x}^{2}$?

The domain and range of $y=\mathrm{sin}x$ is

A)$R,[0,\mathrm{\infty}]$

B)$R,[-1,1]$

C)$R,[-\mathrm{\infty},\mathrm{\infty}]$

D)$R,[1,\mathrm{\infty}]$Mean of the squares of the deviations from mean is called the:

Variance

Standard deviation

Quartile deviation

ModeHow to evaluate P(10,2)?

What is the effect of wind speed on evaporation?

What is the range of a linear function?

Find the range of $\frac{{x}^{2}}{1-{x}^{2}}$

State the main limitations of statistics.

What is the range of the function y = x?

Tell whether the statement is true or false : A data always has a mode.

In most cases,_____variables are not considered to be equal unless they are exactly the same.

A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.

$3+3x3-3+3=?$What is the right answer and how?

Define lateral displacement.