Question

complete the table of values for $f(x) = 4^x$ and $g(x) = x + 8$.

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

both $f(x)$ and $g(x)$ grow as $x$ gets larger and larger. which function eventually exceeds the other?
$f(x) = 4^x$ $g(x) = x + 8$

Explanation:

Step1: Calculate f(x) for x=1

$f(1)=4^1=4$

Step2: Calculate g(x) for x=1

$g(1)=1+8=9$

Step3: Calculate f(x) for x=2

$f(2)=4^2=16$

Step4: Calculate g(x) for x=2

$g(2)=2+8=10$

Step5: Calculate f(x) for x=3

$f(3)=4^3=64$

Step6: Calculate g(x) for x=3

$g(3)=3+8=11$

Step7: Calculate f(x) for x=4

$f(4)=4^4=256$

Step8: Calculate g(x) for x=4

$g(4)=4+8=12$

Step9: Compare long-term growth

Exponential functions grow faster than linear functions.

Answer:

Completed Table:

$x$	$f(x)$	$g(x)$
2	16	10
3	64	11
4	256	12

Growth Comparison Answer:

$f(x) = 4^x$