dripcima24

2022-09-07

How do I find the range of the function $y=-{2}^{x}+2$?

Houston Ellis

Beginner2022-09-08Added 4 answers

Here's my attempt:

y<2 is the range.

$y=-{2}^{x}+2$ Can also be written as

$2-y={2}^{x}$

and also,

$\mathrm{ln}(2-y)=x\mathrm{ln}2$

$\Rightarrow 2-y>0\Rightarrow y<2$

y<2 is the range.

$y=-{2}^{x}+2$ Can also be written as

$2-y={2}^{x}$

and also,

$\mathrm{ln}(2-y)=x\mathrm{ln}2$

$\Rightarrow 2-y>0\Rightarrow y<2$

tun1ju2k1ki

Beginner2022-09-09Added 2 answers

The range of $y=-{2}^{x}+2$ is $(-\mathrm{\infty};2)$

I'd start from a known fact that ${a}^{x}>0$ for all a>0 and $x\in \mathbb{R}$

So:

${2}^{x}>0$

$-{2}^{x}<0$

$-{2}^{x}+2<2$

y<2

$y\in (-\mathrm{\infty};2)$

I'd start from a known fact that ${a}^{x}>0$ for all a>0 and $x\in \mathbb{R}$

So:

${2}^{x}>0$

$-{2}^{x}<0$

$-{2}^{x}+2<2$

y<2

$y\in (-\mathrm{\infty};2)$

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.