Come up with a new linear function that has a slope that falls in the range -1<m<0. Choose two different initial values. For this new linear function,
what happens to the function’s values after many iterations? Are the
function’s values getting close to a particular number in each case?
(The linear function before this was f(4)=1/2*4+1=3 idk if this will help)
Can someone please explain what they are asking or give me an example of what they're asking for?
Certainly! In this question, they are asking you to come up with a new linear function which has a slope that falls within the range -1 < m < 0.
A linear function is typically written as f(x) = mx + c, where m represents the slope and c represents the y-intercept. In this case, they want you to choose a slope (m) that is between -1 and 0.
To come up with a specific example, let's choose m = -0.5. Now we can write our linear function as f(x) = -0.5x + c.
Next, we need to choose two different initial values for x. Let's say x1 = 0 and x2 = 2.
To find the corresponding y-values, we can substitute these values into our linear function. So for x1 = 0, we have f(0) = -0.5(0) + c = c. And for x2 = 2, we have f(2) = -0.5(2) + c = -1 + c.
Now, to answer the second part of the question about what happens to the function's values after many iterations, we can calculate the values for f(x) for a few more iterations.
Let's find f(4) and f(6) for the given examples:
For x = 4: f(4) = -0.5(4) + c = -2 + c.
For x = 6: f(6) = -0.5(6) + c = -3 + c.
As you can see, each time we iterate, the function's values are getting close to a particular number, which is the y-intercept (c). In this case, without knowing the value of c, we cannot determine to which number the function's values are getting closer.