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y=(1)/(2)*((1)/(4))^(x)
Growth / Decay
Domain:
Range:

y-intercept:
Asymptote:

$26$ . $y=\frac{1}{2} \cdot\left(\frac{1}{4}\right)^{x}$ $\newline$ Growth / Decay $\newline$ Domain: $\newline$ Range: $\newline$ $y$ -intercept: $\newline$ Asymptote:

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Reflections of functions

Full solution

Q.

26

.

y=\frac{1}{2} \cdot\left(\frac{1}{4}\right)^{x}

\newline

Growth / Decay

\newline

Domain:

\newline

Range:

\newline

y

-intercept:

\newline

Asymptote:

Exponential Function Type: To determine if the function represents growth or decay, we need to look at the base of the exponential function, which is $(\frac{1}{4})$ in this case. $\newline$ Since $(\frac{1}{4})$ is between $0$ and $1$ , the function represents exponential decay.
Domain: The domain of an exponential function is all real numbers because you can raise a positive number to any power. $\newline$ Domain: $(-\infty, \infty)$
Range: The range of an exponential function is all positive numbers because a positive number raised to any power is positive. Additionally, since the function is multiplied by $(1/2)$ , it will approach $0$ , but it will approach it. $\newline$ Range: $(0, \infty)$
Y-Intercept: To find the y-intercept, we set $x$ to $0$ and solve for $y$ . $\newline$ $y = \frac{1}{2} \times \left(\frac{1}{4}\right)^0$ $\newline$ $y = \frac{1}{2} \times 1$ $\newline$ $y = \frac{1}{2}$ $\newline$ The y-intercept is the point $(0, \frac{1}{2})$ .
Horizontal Asymptote: The horizontal asymptote of an exponential decay function is the value that the function approaches as $x$ goes to infinity. In this case, as $x$ increases, $(\frac{1}{4})^x$ approaches $0$ , and since the function is multiplied by $(\frac{1}{2})$ , the horizontal asymptote is $y = 0$ . $\newline$ Asymptote: $y = 0$

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