Question

Please help me run step by step on solving this as I’m reallyConfused

Answer 1

Given:

The graph of the function is given.

To find:

The correct function.

Explanation:

Graph A:

Since the end behaviours are,

$\begin{gathered} As\text{ x}\rightarrow-\infty,f(x)\rightarrow0 \\ As\text{x}\operatorname{\rightarrow}\infty,f(x)\operatorname{\rightarrow}\infty \end{gathered}$

So, the function is,

$y=2^x$

Graph B:

Since the end behaviours are,

$A\mathrm{s}\:x\to\:+\infty\:,\:f\left(x\right)\to\:-\infty$

So, the function is,

$y=\log_{\frac{1}{2}}x$

Graph C:

Since the end behaviours are,

$\begin{gathered} A\mathrm{s}\:x\to\:+\infty\:,\:f\left(x\right)\to\:0 \\ A\mathrm{s}\:x\to\:-\infty\:,\:f\left(x\right)\to\:+\infty \end{gathered}$

So, the function is,

$y=(\frac{1}{2})^x$

Graph D:

Since the end behaviours are,

$A\mathrm{s}\:x\to\:+\infty\:,\:f\left(x\right)\to\:+\infty\:$

So, the function is,

$y=\log_2x$