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The table shows values for the function f, while the graph shows function g.

Which function has the greater slope?
Responses
A f
B g
C They are the same.
D Insufficient information.

3 answers

To determine which function has the greater slope, you need to analyze both the values provided in the table for function \( f \) and the graph for function \( g \).

  1. For function \( f \): The slope can be calculated between two points using the formula: \[ \text{slope} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} \] You'll need to take two or more points from the table to find the slope.

  2. For function \( g \): You can observe the graph and determine the slope visually by finding the rise over run between two points on the graph. Again, use the formula above for any two points on the graph.

Once you have computed or estimated the slopes for both functions, compare the values:

  • If the slope of function \( f \) is greater than that of function \( g \), the answer is A (f).
  • If the slope of function \( g \) is greater than that of function \( f \), the answer is B (g).
  • If both slopes are equal, the answer is C (They are the same).
  • If you can't determine the slope from the given information, the answer is D (Insufficient information).

Without specific values or a visual of the graph, I can't provide a definitive answer. You would need to follow the steps above to analyze the functions. If you provide more details or data, I can help further!

x y
1 4
3 10
5 16
7 22
9 28

Given the values from the table for function \( f \):

\[ \begin{align*} x & : 1, 3, 5, 7, 9 \ y & : 4, 10, 16, 22, 28 \ \end{align*} \]

We can calculate the slope of function \( f \). The slope between any two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's calculate the slope between a couple of points from the table.

  1. Between the points (1, 4) and (3, 10): \[ \text{slope} = \frac{10 - 4}{3 - 1} = \frac{6}{2} = 3 \]

  2. Between the points (3, 10) and (5, 16): \[ \text{slope} = \frac{16 - 10}{5 - 3} = \frac{6}{2} = 3 \]

  3. Between the points (5, 16) and (7, 22): \[ \text{slope} = \frac{22 - 16}{7 - 5} = \frac{6}{2} = 3 \]

  4. Between the points (7, 22) and (9, 28): \[ \text{slope} = \frac{28 - 22}{9 - 7} = \frac{6}{2} = 3 \]

So the slope of function \( f \) is consistently 3.

Now, regarding function \( g \), since you mentioned that there is a graph available, you would need to visually observe or calculate the slope from that graph. If you can say that the slope of function \( g \) is either greater than, less than, or equal to 3 based on the graph, you can come to a conclusion.

  • If the slope of \( g \) is greater than 3, the answer would be B (g).
  • If the slope of \( g \) is less than 3, the answer would be A (f).
  • If the slope of \( g \) is exactly 3, the answer would be C (They are the same).
  • If you can't determine the slope from the graph, the answer would be D (Insufficient information).

Please check the graph for the slope of function \( g \) to finalize your answer!