Question

complete the table of values for $f(x) = 2x + 3$ and $g(x) = 2^x + 1$.

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

both $f(x)$ and $g(x)$ grow as $x$ gets larger and larger. which function eventually exceeds the other?
$f(x) = 2x + 3$ $g(x) = 2^x + 1$

Explanation:

Step1: Calculate f(x) for x=1

Substitute x=1 into $f(x)=2x+3$:
$2(1)+3=5$

Step2: Calculate g(x) for x=1

Substitute x=1 into $g(x)=2^x+1$:
$2^1+1=3$

Step3: Calculate f(x) for x=2

Substitute x=2 into $f(x)=2x+3$:
$2(2)+3=7$

Step4: Calculate g(x) for x=2

Substitute x=2 into $g(x)=2^x+1$:
$2^2+1=5$

Step5: Calculate f(x) for x=3

Substitute x=3 into $f(x)=2x+3$:
$2(3)+3=9$

Step6: Calculate g(x) for x=3

Substitute x=3 into $g(x)=2^x+1$:
$2^3+1=9$

Step7: Calculate f(x) for x=4

Substitute x=4 into $f(x)=2x+3$:
$2(4)+3=11$

Step8: Calculate g(x) for x=4

Substitute x=4 into $g(x)=2^x+1$:
$2^4+1=17$

Step9: Compare long-term growth

Exponential functions grow faster than linear functions.

Answer:

Completed Table:

$x$	$f(x)$	$g(x)$
2	7	5
3	9	9
4	11	17

Growth Comparison Answer:

$g(x)=2^x + 1$