Mathematics: Can y’all me answer these questions

You have to look at the tenths place (the first 8) then look it the digit on the right (the second 8) because it is bigger than 5 you round it up so, the answer is 5.9...

Can y’all me answer these questions - id4014720, daniella1304

Ответ:

rleiphart1

11.01.2022

Mathematics

2. $f(x)=\dfrac18\left(\dfrac14\right)^{x-2}$

Domain: $(-\infty,\infty)$ , because any value of is allowed and gives a number f(x) .

Range: $(0,\infty)$ , because a^x0 for any positive real $a\neq0$ .

y-intercept: This is a point of the form (0, f(0)) . So plug in x=0 ; we get $f(0)=\frac18\left(\frac14\right)^{-2}=\frac{4^2}8=2$ . So the intercept is (0, 2), or just 2. (Interestingly, you didn't get marked wrong for that...)

Asymptote: This can be deduced from the range; the asymptote is the line y=0 .

Increasing interval: Going from left to right, there is no interval on which f(x) is increasing, since 1/4 is between 0 and 1.

Decreasing interval: Same as the domain; f(x) is decreasing over the entire real line.

End behavior: The range tells you f(x)0 , and you know f(x) is decreasing over its entire domain. This means that $f(x)\to+\infty$ as $x\to-\infty$ , and $f(x)\to0$ and $x\to+\infty$ .

3. $f(x)=\left(\dfrac32\right)^{-x}-7$

Domain: Same as (2), $(-\infty, \infty)$ .

Range: We can rewrite $f(x)=\left(\frac23\right)^x-7$ . $\left(\frac23\right)^x0$ for all , so $\left(\frac23\right)^x-7-7$ for all . Then the range is $(-7,\infty)$ .