Question

complete the table of values (for ( f(x) = 4x^2 - 6 ) and ( g(x) = 5x - 2 ))

( x )	( f(x) )	( g(x) )
2
3
4

both ( f(x) ) and ( g(x) ) grow as ( x ) gets larger and larger. which function eventually exceeds the other?
( f(x) = 4x^2 - 6 )
( g(x) = 5x - 2 )

Explanation:

Step1: Calculate $f(x)$ for $x=1$

Substitute $x=1$ into $f(x)=4x^2-6$:
$f(1)=4(1)^2-6=4-6=-2$

Step2: Calculate $g(x)$ for $x=1$

Substitute $x=1$ into $g(x)=5x-2$:
$g(1)=5(1)-2=5-2=3$

Step3: Calculate $f(x)$ for $x=2$

Substitute $x=2$ into $f(x)=4x^2-6$:
$f(2)=4(2)^2-6=16-6=10$

Step4: Calculate $g(x)$ for $x=2$

Substitute $x=2$ into $g(x)=5x-2$:
$g(2)=5(2)-2=10-2=8$

Step5: Calculate $f(x)$ for $x=3$

Substitute $x=3$ into $f(x)=4x^2-6$:
$f(3)=4(3)^2-6=36-6=30$

Step6: Calculate $g(x)$ for $x=3$

Substitute $x=3$ into $g(x)=5x-2$:
$g(3)=5(3)-2=15-2=13$

Step7: Calculate $f(x)$ for $x=4$

Substitute $x=4$ into $f(x)=4x^2-6$:
$f(4)=4(4)^2-6=64-6=58$

Step8: Calculate $g(x)$ for $x=4$

Substitute $x=4$ into $g(x)=5x-2$:
$g(4)=5(4)-2=20-2=18$

Step9: Compare long-term growth

Quadratic functions grow faster than linear functions as $x$ increases.

Answer:

Completed Table:

$x$	$f(x)$	$g(x)$
2	10	8
3	30	13
4	58	18

Growth Conclusion:

$f(x) = 4x^2 - 6$ eventually exceeds $g(x) = 5x - 2$ as $x$ gets larger.