Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
-$$f ( x ) = ( x - 3 ) ^ { 3 }$$
A) above the $x$-axis: $( 3 , \infty )$
below the $x$-axis: $( - \infty , 3 )$

B) above the $x$-axis: $( - \infty , 3 )$
below the $x$-axis: $( 3 , \infty )$

C) above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , 3 ) , ( 3 , \infty )$

D) above the $x$-axis: $( - \infty , 3 ) , ( 3 , \infty )$
below the $x$-axis: no intervals

Question

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis.
-$$f ( x ) = ( x - 3 ) ^ { 3 }$$
A) above the $x$-axis: $( 3 , \infty )$
below the $x$-axis: $( - \infty , 3 )$

B) above the $x$-axis: $( - \infty , 3 )$
below the $x$-axis: $( 3 , \infty )$

C) above the $x$-axis: no intervals
below the $x$-axis: $( - \infty , 3 ) , ( 3 , \infty )$

D) above the $x$-axis: $( - \infty , 3 ) , ( 3 , \infty )$
below the $x$-axis: no intervals

Quizplus · Accepted Answer

The function $f(x) = (x - 3)^3$ has a single x-intercept at $x = 3$. Since the exponent is odd, the function changes sign across this intercept. For $x < 3$, $f(x)$ is negative (below the x-axis), and for $x > 3$, $f(x)$ is positive (above the x-axis).

Use the X-Intercepts to Find the Intervals on Which the Graph