Question

checkpoint1.6.1
algebra ii - s2: module 8: lesson 110
7 which function is represented by this graph?
$\bigcirc y = 5\sqrt{x}$
$\bigcirc y = x\sqrt{5}$
$\bigcirc y = \sqrt{5x}$
$\bigcirc y = 5x\sqrt{x}$

Explanation:

Step1: Identify a point on the graph

The graph passes through $(5, 5)$.

Step2: Test point in Option 1

Substitute $x=5, y=5$ into $y=5\sqrt{x}$:
$5=5\sqrt{5} \approx 11.18$, false.

Step3: Test point in Option 2

Substitute $x=5, y=5$ into $y=x\sqrt{5}$:
$5=5\sqrt{5} \approx 11.18$, false.

Step4: Test point in Option 3

Substitute $x=5, y=5$ into $y=\sqrt{5x}$:
$5=\sqrt{5\times5}=\sqrt{25}=5$, true.

Step5: Verify with another point

Graph passes through $(1, \sqrt{5})\approx(1,2.24)$. Substitute $x=1$ into $y=\sqrt{5x}$:
$y=\sqrt{5\times1}=\sqrt{5}\approx2.24$, matches the graph.

Answer:

$\boldsymbol{y=\sqrt{5x}}$