Question

complete the sentences about the functions $f(x) = 5x + 12$ and $g(x) = 3(2)^x$.

for small values of $x$, the function with greater values is . for instance, whereas . as the value of $x$ increases, however, eventually has greater values.

Explanation:

Step1: Test small x (e.g., x=0)

Calculate $f(0)=5(0)+12=12$, $g(0)=3(2)^0=3(1)=3$

Step2: Compare small x values

$12>3$, so $f(x)$ is larger here.

Step3: Test larger x (e.g., x=4)

Calculate $f(4)=5(4)+12=20+12=32$, $g(4)=3(2)^4=3(16)=48$

Step4: Compare large x values

$48>32$, so $g(x)$ becomes larger.

Answer:

For small values of $x$, the function with greater values is $\boldsymbol{f(x) = 5x + 12}$. For instance, $\boldsymbol{f(0)=12}$ whereas $\boldsymbol{g(0)=3}$. As the value of $x$ increases, however, $\boldsymbol{g(x) = 3(2)^x}$ eventually has greater values.