To determine the true statements regarding the represented function, you need to analyze the graph of the function. Here's how you can interpret each statement based on the graph:
1. **f(x) > 0 over the interval (1, infinity)**: This means that for all values of x greater than 1, the function f(x) is positive (above the x-axis).
2. **f(x) ≤ 0 over the interval [1, infinity)**: This means that for all values of x from 1 to infinity, including x = 1, the function f(x) is either zero or negative (at or below the x-axis).
3. **f(x) ≥ 0 over the interval (-infinity, 1]**: This means that for all values of x from negative infinity up to and including 1, the function f(x) is either zero or positive (at or above the x-axis).
4. **f(x) > 0 over the interval (-infinity, 1)**: This means that for all values of x less than 1, the function f(x) is positive (above the x-axis).
5. **f(x) > 0 over the interval (-infinity, infinity)**: This means that for all values of x, the function f(x) is positive (above the x-axis) over the entire domain.
Without the actual graph, I can't definitively determine which statements are true. However, to complete this exercise, you would need to visually inspect the graph of the function and check for the following:
- Positive values of f(x) (points where the graph is above the x-axis).
- Intervals where f(x) is zero or negative (points where the graph touches or is below the x-axis).
Based on a general analysis you'd check:
- Statement 1 is true if the graph is entirely above the x-axis for x > 1.
- Statement 2 is true if the graph is entirely on or below the x-axis starting from x = 1.
- Statement 3 is true if the graph is entirely above the x-axis up to and including x = 1.
- Statement 4 is true if the graph is entirely above the x-axis for x < 1.
- Statement 5 is true if the graph is entirely above the x-axis for all x (a globally positive function).
Check the graph accordingly and mark all that apply.
Use the graphing tool to determine the true statements regarding the represented function. Check all that apply.
f(x) > 0 over the interval (1, infinity).
f(x) 0 over the interval [1, infinity).
f(x) 0 over the interval (-infinity, 1].
f(x) > 0 over the interval (-infinity, 1).
f(x) > 0 over the interval (-infinity, infinity).
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