Question

Consider f(x) = 3 square root 2 -x

(The rest of the question is in photo!) PLSSSS it’s timed

Answer 1

Answer: See below

Explanation:

`\begin{array}{l}f\left(x\right)=3√(-x+2\ )\\\\Domain:\ \text{Case 1:}\ √(-x+2\ )\\\\\ x\ +\ 2\ \ge\ 0\ \\=-x\ \ge-2\\=\ x\ \le2\\\\\text{Case 2}:\ -x\ +\ 2\ \longrightarrow\ x\in\mathbb{R}\\\\\therefore\left(-\infty,\ 2\right]\end{array}`

You can use Desmos so no need for complicated math

HA = None

VA = None

x-intercept = 2 - (2, 0)

y-intercept (exact value, Desmos only gives decimals)

f(0)=3√2-(0)

f(0)=3√2 <-- y-intercept (0, 3√2)

End behavior: Graph of f(x) moving to the left, but slowly going upwards, x-values decreasing but y-values increasing so
`\mathrm{as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:\\`