Question

The linear function f(x) passes through the points (0, 3) and (2, 7). A few values from the exponential function g(x)are shown in the table. X g(x) â’1 23 2 18 3 54 What is the positive difference in the y-intercept value of ​f(x)​and g(x)​? Enter your answer in the box.

Answer 1

The positive difference in the y-intercept values of f(x) and g(x) is 3 - 23 = -20.

Step-by-step explanation:

To find the positive difference in the y-intercept values of f(x) and g(x), we need to determine the y-intercepts of both functions. The linear function f(x) can be represented as y = mx + b, where m is the slope and b is the y-intercept. Given the points (0, 3) and (2, 7), we can substitute the values to find the slope, which is m = Δy / Δx = (7 - 3) / (2 - 0) = 2. Now, we can substitute the slope and one of the points into the equation to solve for b. Plugging in the values, we get 3 = (2)(0) + b. Solving for b, we find that the y-intercept of f(x) is 3.

For the exponential function g(x), we are given a table of values. Since the table doesn't include the y-intercept, we can't determine its value directly. However, we can observe that the values of g(x) decrease as x increases, indicating that the function is likely to have a positive y-intercept. Therefore, it's safe to assume that the positive difference in the y-intercept values of f(x) and g(x) is 3 - 23 = -20.