Question

consider continuous functions f and g. then complete the statement.
function g is the sum of 2 and
the cube root of the sum of
three times x and 1.
select the correct answer from each drop - down.
the x - intercept of function f is the x - intercept of function g.

Explanation:

Step1: Find x-intercept of f

The x-intercept of a function is where its output is 0. From the table, when $f(x)=0$, $x=3$.

Step2: Define function g

Translate the description to an equation:
$g(x) = 2 + \sqrt[3]{3x + 1}$

Step3: Find x-intercept of g

Set $g(x)=0$ and solve for $x$:
$0 = 2 + \sqrt[3]{3x + 1}$
$\sqrt[3]{3x + 1} = -2$
Cube both sides:
$3x + 1 = (-2)^3 = -8$
$3x = -8 - 1 = -9$
$x = \frac{-9}{3} = -3$

Step4: Compare the two intercepts

Compare $3$ and $-3$: $3 > -3$.

Answer:

greater than