Question

select all the statements about the function in graph that are true. some input values are negative. some input values are integers. there will never be an output value of zero. some output values are integers. some output values are negative.

Explanation:

1. Some input values are negative: The graph extends left into negative x-values, so this is true.
2. Some input values are integers: The line passes through x-values like -4, -2, 0, 2, 4 (integers), so this is true.
3. There will never be an output value of zero: To check, find when y=0. The line has equation $y=\frac{1}{3}x - 4$. Set $0=\frac{1}{3}x - 4$, solve for $x$: $x=12$, so y=0 when x=12. This statement is false.
4. Some output values are integers: The line passes through points like (0, -4) and (3, -3), so y-values include integers. This is true.
5. Some output values are negative: The line is below the x-axis for all x < 12, so negative y-values exist. This is true.

Answer:

• Some input values are negative.
• Some input values are integers.
• Some output values are integers.
• Some output values are negative.