How do you graph $y = \frac{1}{4} \sqrt{x - 1} + 2$ $y=1/4sqrt(x-1)+2$ , compare to the parent graph, and state the domain and range?

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Answer 1 · 2018-01-04T16:57:47

$D_{f} = [1, + \infty)$ $D_f=[1,+oo)$ , $R_{f} = [2, + \infty)$ $R_f=[2,+oo)$

graph{sqrt(x-1)/4+2 [-10, 10, -5, 5]}

The graph is $\sqrt{x}$ $sqrtx$ shifted $1$ $1$ to the right and what comes out of that shifted $2$ $2$ times upwards.

$D_{f}$ $D_f$ $=$ $=$ ${\forall x$ ${AAx$ $\in$ $in$ $RR$ : $x-1>=0$ $}$ $=$ $[1,+oo)$

I will find the range using Monotony and continuity.

$f(x)=1/4sqrt(x-1)+2$ ,
$x>=1$

$f'(x)=1/4*((x-1)')/(2sqrt(x-1))$ $=$

$1/(8sqrt(x-1))$ $>0$ , $x$ $in$ $(1,+oo)$

Therefore $f$ is strictly increasing $uarr$ in $[1,+oo)$

$=$ $[2,+oo)$

because $lim_(xrarr+oo)f(x)=lim_(xrarr+oo)(sqrt(x-1)/4+2)$ $=$ $+oo$

NOTE: $lim_(xrarr+oo)(x-1)=+oo$ therefore, $lim_(xrarr+oo)sqrt(x-1)=+oo$

How do you graph y=1/4sqrt(x-1)+2y=14√x−1+2y=1/4sqrt(x-1)+2, compare to the parent graph, and state the domain and range?