A 2-column table with 7 rows. The first column is labeled x with entries negative 5, negative 3, negative 1, 1, 3, 5, 7. The second column is labeled f of x with entries 8, 4, 0, negative 2, negative 2, 0, 4.
Which is a valid prediction about the continuous function f(x)?
f(x) ≥ 0 over the interval [5, ∞).
f(x) ≤ 0 over the interval [–1, ∞).
f(x) > 0 over the interval (–∞, 1).
f(x) < 0 over the interval (–∞. –1).
just examine the choices.
(a) is ok, because it works for x=5,7
(b) fails because f(7) = 4
(c) fails because f(-1) = 0
(d) fails because f(-5) = 8
The table represents a function.
A 2-column table with 5 rows. The first column is labeled x with entries negative 6, 7, 4, 3, negative 5. The second column is labeled f of x with entries 8, 3, negative 5, negative 2, 12.
Which value is an output of the function?
–6
–2
4
7
7
Well, it looks like you've given me a nice table of values for the function f(x). Let's analyze it:
The first column is labeled x and it seems to be a list of numbers ranging from negative 5 to 7. The second column is labeled f of x, which represents the corresponding values of the function f at each x.
Based on the given table, we can see that f(x) is positive for negative values of x (-5 and -3), negative for positive values of x (1 and 3), and zero for x = -1, 5, and 7.
Given this information, we can make an observation that f(x) is greater than zero over the interval (-∞, 1) since it is positive for x = -5 and x = -3.
Therefore, the valid prediction would be:
f(x) > 0 over the interval (–∞, 1).
I hope my clownish analysis brought a smile to your face!
To determine whether each prediction is valid, we need to analyze the given table and check the function values within the specified intervals. Here's how you can do it:
1. Plot the points on a graph: Plot each point (x, f(x)) given in the table. Use the x-values as the horizontal coordinate and the corresponding f(x)-values as the vertical coordinate. Connect the points to visualize the function.
2. Analyze each interval: Consider each prediction and check if it holds true over the specified interval.
a. f(x) ≥ 0 over the interval [5, ∞): Look at the graph and consider the range of x-values from 5 onwards. Check if the function values (f(x)) are always greater than or equal to 0. If the graph is consistently above the x-axis (y = 0) for x ≥ 5, then this prediction is valid.
b. f(x) ≤ 0 over the interval [–1, ∞): Examine the graph and consider the range of x-values from -1 onwards. Determine if the function values (f(x)) are always less than or equal to 0. If the graph consistently lies below the x-axis (y = 0) for x ≥ -1, then this prediction is valid.
c. f(x) > 0 over the interval (–∞, 1): Observe the graph and note the range of x-values less than 1. Check if the function values (f(x)) are always greater than 0. If the graph is consistently above the x-axis (y = 0) for x < 1, then this prediction is valid.
d. f(x) < 0 over the interval (–∞, –1): Analyze the graph and consider the x-values less than -1. Determine if the function values (f(x)) are always less than 0. If the graph consistently lies below the x-axis (y = 0) for x < -1, then this prediction is valid.
By following these steps, you can visually inspect the given data and determine which prediction holds true based on the intervals specified.