Question

complete the table of values for $f(x) = 5x^2 - 6$ and $g(x) = 7x$.

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

both $f(x)$ and $g(x)$ grow as $x$ gets larger and larger. which function eventually exceeds the other?
$f(x) = 5x^2 - 6$ $g(x) = 7x$

Explanation:

Step1: Calculate f(1) and g(1)

$f(1)=5(1)^2 - 6 = 5 - 6 = -1$
$g(1)=7(1)=7$

Step2: Calculate f(2) and g(2)

$f(2)=5(2)^2 - 6 = 20 - 6 = 14$
$g(2)=7(2)=14$

Step3: Calculate f(3) and g(3)

$f(3)=5(3)^2 - 6 = 45 - 6 = 39$
$g(3)=7(3)=21$

Step4: Calculate f(4) and g(4)

$f(4)=5(4)^2 - 6 = 80 - 6 = 74$
$g(4)=7(4)=28$

Step5: Compare long-term growth

Quadratic functions ($x^2$) grow faster than linear functions ($x$) as $x$ increases.

Answer:

Completed Table:

$x$	$f(x)$	$g(x)$
2	14	14
3	39	21
4	74	28

Growth Comparison:

$f(x) = 5x^2 - 6$