Question

identify the features of functions f and g by sorting the statements to the functions they describe. press on an item in the answer box, and then press on the box under the corresponding category. to remove an item, you can press on the box and the trash can icon to the right of the item you want to remove. f(x) add an answer item g(x) add an answer item f(x) and g(x) add an answer item answer bank the function is increasing until x is 6. the function has a maximum value of 8. the function is decreasing for the entirety of the graph. the function has a horizontal intercept. the function has a vertical intercept.

Explanation:

1. For $f(x)$: Observe the parabola opens downward, so it has a maximum at its vertex $(6, 8)$. It increases from $x=0$ to $x=6$, and crosses the x-axis at $(0,0)$ (horizontal intercept) and crosses the y-axis at $(0,0)$ (vertical intercept).
2. For $g(x)$: Observe the straight line has a negative slope, so it decreases across its entire domain. It crosses the y-axis at $(0,8)$ (vertical intercept) and crosses the x-axis at $(12,0)$ (horizontal intercept).
3. Both functions have horizontal and vertical intercepts, so these statements apply to both.

Answer:

$f(x)$:

• The function is increasing until $x$ is 6.
• The function has a maximum value of 8.

$g(x)$:

• The function is decreasing for the entirety of the graph.

$f(x)$ and $g(x)$:

• The function has a horizontal intercept.
• The function has a vertical intercept.