Question

over what interval is the function shown in the table increasing?
$f(x) = 3x^2$

$x$	$f(x)$	$(x,y)$
$-1$	$3$	$(-1,3)$
$0$	$0$	$(0,0)$
$1$	$3$	$(1,3)$
$2$	$12$	$(2,12)$

a. $x > -2$
b. $x < 0$
c. $x > 0$
d. $x < 2$

Explanation:

Step1: Identify decreasing interval

A function decreases when as $x$ increases, $f(x)$ decreases.
Check $x$ values: $-2 \to -1 \to 0$: $f(x)$ goes from $12 \to 3 \to 0$ (decreasing). $0 \to 1 \to 2$: $f(x)$ goes from $0 \to 3 \to 12$ (increasing).

Step2: Match to interval

The decreasing part is when $x$ is less than 0, since for $x<0$, increasing $x$ leads to lower $f(x)$.

Answer:

B. $x<0$