With some functions, the value of the

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

3 0

Answer and explanation:

This is an example of negative correlation/inverse relationship between two variables. A negative correlation between two variables, independent and dependent variable, occurs when increase in one variable is associated with decrease in the other. In other words, the two variables tend to go in opposite direction.

The independent variable is the variable that causes a change in the dependent variable. For example, an increase in the independent variable in an inverse relationship will bring about a decrease in the dependent variable.

A good real world example is the increase in inflation and the decrease in purchasing power of money.

An equation for this could be

Y=-0.2(x)

Where y is dependent variable purchasing power and x is independent variable inflation

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Can y’all help me answer these questions

cupoosta [38]

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

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

Range: $(0,\infty)$ , because $a^x>0$ 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 $f(x)=\left(\frac23\right)^x-7$ . $\left(\frac23\right)^x>0$ for all $x$ , so $\left(\frac23\right)^x-7>-7$ for all $x$ . Then the range is $(-7,\infty)$ .