Question

graphing the cube root parent function
this is the graph of the function $y = \sqrt3{x}$.
fill in the $y$-values of the t-table for the function $y = \sqrt3{x}$.

$x$	$y$
$-1$	$\square$
$0$	$\square$
$1$	$\square$
$8$	$\square$

Explanation:

Step1: For \( x = -8 \)

We need to find \( y = \sqrt[3]{-8} \). Since \( (-2)^3 = -8 \), so \( \sqrt[3]{-8} = -2 \).

Step2: For \( x = -1 \)

Find \( y = \sqrt[3]{-1} \). As \( (-1)^3 = -1 \), then \( \sqrt[3]{-1} = -1 \).

Step3: For \( x = 0 \)

Calculate \( y = \sqrt[3]{0} \). Since \( 0^3 = 0 \), so \( \sqrt[3]{0} = 0 \).

Step4: For \( x = 1 \)

Find \( y = \sqrt[3]{1} \). Because \( 1^3 = 1 \), then \( \sqrt[3]{1} = 1 \).

Step5: For \( x = 8 \)

Calculate \( y = \sqrt[3]{8} \). As \( 2^3 = 8 \), so \( \sqrt[3]{8} = 2 \).

Answer:

For \( x = -8 \), \( y = -2 \); for \( x = -1 \), \( y = -1 \); for \( x = 0 \), \( y = 0 \); for \( x = 1 \), \( y = 1 \); for \( x = 8 \), \( y = 2 \). So the filled table has \( y \)-values (from top to bottom) \(-2\), \(-1\), \(0\), \(1\), \(2\).