Question

the square root function
use the graphing calculator to graph the function $f(x) = -\sqrt{x}$. which list contains three points that lie on the graph of
the function?
$(1, -1)$, $(4, -2)$, $(9, -3)$
$(1, 1)$, $(4, 2)$, $(9, 3)$
$(-9, 3)$, $(-4, 2)$, $(-1, 1)$
$(-9, -3)$, $(-4, -2)$, $(-1, -1)$

Explanation:

Step1: Recall the function

The function is \( f(x) = -\sqrt{x} \). The domain of the square root function \( \sqrt{x} \) is \( x \geq 0 \), so we can eliminate options with negative \( x \)-values (third and fourth options since they have \( x = -9, -4, -1 \)).

Step2: Test points in first two options

For the first option:

• When \( x = 1 \), \( f(1) = -\sqrt{1} = -1 \), so \( (1, -1) \) is on the graph.
• When \( x = 4 \), \( f(4) = -\sqrt{4} = -2 \), so \( (4, -2) \) is on the graph.
• When \( x = 9 \), \( f(9) = -\sqrt{9} = -3 \), so \( (9, -3) \) is on the graph.

For the second option:

• When \( x = 1 \), \( f(1) = -\sqrt{1} = -1

eq 1 \), so \( (1, 1) \) is not on the graph.

Answer:

\((1, -1)\), \((4, -2)\), \((9, -3)\)