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) −1 23 2 18 3 54 what is the positive difference in the y-intercept value of f(x) and g(x) ?

1

Step-by-step explanation:

The y-intercept of any function is the point where it crosses through the y-axis.  Since the x-value for every point on the y-axis is 0, this means the y-intercept will have an x-coordinate of 0.  For the linear function, f(x), the y-intercept is (0, 3).

We are missing some values of the exponential function.  We have (-1, 2/3), (2, 18), and (3, 54).

We know it is exponential, which means we know that the y-value of each point is multiplied by a constant to get the next y-value.  Comparing (2, 18) and (3, 54), we see that the y-values are multiplied by 3.

Working backward from this, we figure out that the y-value for the point with an x-coordinate of 1 will be 18/3 = 6.  

The y-coordinate of the point with an x-coordinate of 0 will be 6/3 = 2.

This means the y-intercept of the function g(x) will be (0, 2).

This makes the difference between the y-intercepts 3-2 = 1.