The image contains a graph and instructions for determining intercepts. The graph shows an orange curve that intersects the y-axis between 0 and 20, and the x-axis between 0 and 2. The instructions ask to use the graphing tool to find the x-intercept and y-intercept.

Answer 1

To find the intercepts from the graph described:

1. Y-intercept: This is the point where the curve intersects the y-axis. According to your description, it appears to intersect between 0 and 20. You can estimate the y-intercept by looking at where the curve crosses the vertical line (y-axis). For a precise value, you could read the exact coordinate from the graph.

2. X-intercept: This is the point where the curve intersects the x-axis. Your description indicates it intersects the x-axis between 0 and 2. Again, you would look closely at the intersection point with the horizontal line (x-axis) to determine the exact coordinate.

If you can use a graphing tool, you may be able to input the function directly or use features of the tool to calculate these intercepts automatically. Make sure to read the values where the curve touches the axes accurately for your final answer.

Answer 2

0,-12
3,-12
or 3,0 for X

for Y pick either -1,-20
0,-12
3,-12

Answer 3

Based on the information you've provided, it seems you've identified several points related to the graph:

1. X-Intercepts:

   • The possible x-intercepts you've mentioned include:
     • \( (0, -12) \)
     • \( (3, 0) \) (This would be the valid x-intercept since it lies on the x-axis where \( y = 0 \).)

   Thus, the x-intercept is:

   • \( (3, 0) \)

2. Y-Intercepts:

   • The possible y-intercepts include:
     • \( (0, -20) \)
     • \( (0, -12) \)
     • \( (3, -12) \) (Not a y-intercept since \( x \neq 0 \).)

   So, the y-intercept can be either:

   • \( (0, -20) \) or \( (0, -12) \) depending on where the curve crosses the y-axis.

To summarize:

• The x-intercept is \( (3, 0) \).
• The y-intercept can be either \( (0, -20) \) or \( (0, -12) \), depending on the exact position of the curve on the y-axis.

Choose the y-intercept based on where the curve actually crosses the y-axis.

Answer 4

Use the graphing tool to determine the intercepts.



x-intercept =
✔ (3, 0)



y-intercept =
✔ (0, –12)

The image shows a graph of a function ( f(x) ) and a multiple-choice question. The graph is plotted on a coordinate plane with the x-axis ranging from approximately -3 to 4 and the y-axis from approximately -20 to 20. The function crosses the x-axis at the point (-3, 0).

The multiple-choice question asks about the intervals where ( f(x) ) is greater than or less than zero. The options are:

( f(x) > 0 ) over the interval ((-∞, -3)).
( f(x) > 0 ) over the interval ((-∞, ∞)).
( f(x) < 0 ) over the interval ((-∞, -3)).
( f(x) < 0 ) over the interval ((-∞, ∞)).

Answer 5

Given the information provided about the graph of the function \( f(x) \), let's address the multiple-choice question regarding the intervals where \( f(x) \) is greater than or less than zero.

X-Intercept

You mentioned that the function \( f(x) \) crosses the x-axis at the point (-3, 0). This point indicates where the function transitions from positive values (above the x-axis) to negative values (below the x-axis).

Analyzing the Intervals

1. When \( f(x) > 0 \):

   • Since \( f(x) \) crosses the x-axis at (-3, 0), it implies that the function is positive (above the x-axis) to the left of -3.
   • Thus, \( f(x) > 0 \) over the interval \((-∞, -3)\).

2. When \( f(x) < 0 \):

   • The function turns negative (below the x-axis) from the point -3 onward.
   • Therefore, \( f(x) < 0 \) over the interval \((-3, ∞)\).

Given the options provided, here is how they match up:

• \( (f(x) > 0) \) over the interval \((-∞, -3)\) — This is correct.
• \( (f(x) > 0) \) over the interval \((-∞, ∞)\) — This is incorrect.
• \( (f(x) < 0) \) over the interval \((-∞, -3)\) — This is incorrect.
• \( (f(x) < 0) \) over the interval \((-∞, ∞)\) — This is incorrect, as the function is not negative for all x.

Conclusion

The correct answer from the choices given is:

• \( f(x) > 0 \) over the interval \((-∞, -3)\).

Answer 6

f(x) < 0 over the interval (–infinity, 3).

As the x-values go to positive infinity, the function’s values go to positive infinity.
As the x-values go to negative infinity, the function’s values go to negative infinity.
As the x-values go to positive infinity, the function’s values are equal to 0.

Use the graph to determine the true statement about the end behavior of the function.
The image shows a graph on a coordinate plane with the x-axis labeled as ‘x’ and the y-axis labeled as ‘y’. The graph depicts an orange curve, likely a polynomial function, with distinct turning points. The x-axis ranges from -5 to 5 and the y-axis from -30 to 30. The curve has three turning points: one between -4 and -2, another between -2 and 0, and the third between 2 and 4. The function reaches local maximums at these turning points and has a local minimum between 0 and 2 where it crosses below the x-axis.

Answer 7

Based on your description of the graph and the behavior of the function \( f(x) \), let's analyze the end behavior of the function as \( x \) approaches positive and negative infinity.

Key Points to Consider:

1. As \( x \) approaches negative infinity:

   • You mentioned that the function's values go to negative infinity. This suggests that the left end of the graph is in the third or fourth quadrant, indicating the function is decreasing as \( x \) approaches negative values.

2. As \( x \) approaches positive infinity:

   • You stated that the function's values go to positive infinity. This indicates that the right end of the graph rises upward, suggesting that the ends of the graph go up as \( x \) increases.

Analyzing the Statements:

Based on these interpretations, let's evaluate the statements you provided:

1. As the x-values go to positive infinity, the function’s values go to positive infinity:

   • This statement is true since you observed that the function rises as \( x \) approaches positive infinity.

2. As the x-values go to negative infinity, the function’s values go to negative infinity:

   • This statement is also true based on your observation that the function decreases and approaches negative infinity as \( x \) decreases.

3. As the x-values go to positive infinity, the function’s values are equal to 0:

   • This statement is false because the graph rises towards positive infinity rather than leveling out at 0.

Conclusion:

From your observations, the correct statements regarding the end behavior of the function are:

• As \( x \) approaches positive infinity, the function’s values go to positive infinity.
• As \( x \) approaches negative infinity, the function’s values go to negative infinity.

Given the context, it seems that the true statement regarding the end behavior of the function is the first statement: "As the x-values go to positive infinity, the function’s values go to positive infinity."