Question

which of these key features are correct? select all that apply.

x	f(x)
-1	6
0	8
1	6
2	0

• the function is increasing from $-2 \leq x \leq 0$.
• the function is negative from $-2 \leq x \leq 0$.
• there is a $y$-intercept at $(-2, 0)$.
• there is an $x$-intercept at $(2, 0)$.
• there is a $y$-intercept at $(0, 8)$.
• there is an $x$-intercept at $(0, 8)$.

Explanation:

1. Check if increasing on $-2 \leq x \leq 0$: As $x$ goes from -2 to 0, $f(x)$ goes from 0 to 8 (values rise), so this is true.
2. Check if negative on $-2 \leq x \leq 0$: All $f(x)$ values here are 0, 6, 8 (non-negative), so this is false.
3. Check y-intercept at $(-2,0)$: Y-intercepts occur at $x=0$, so this is false.
4. Check x-intercept at $(2,0)$: X-intercepts are where $f(x)=0$, which matches the table, so this is true.
5. Check y-intercept at $(0,8)$: Y-intercepts are where $x=0$, and $f(0)=8$, so this is true.
6. Check x-intercept at $(0,8)$: X-intercepts require $f(x)=0$, but $f(0)=8$, so this is false.

Answer:

• The function is increasing from $-2 \leq x \leq 0$.
• There is an x-intercept at $(2,0)$.
• There is a y-intercept at $(0,8)$.