Question

Rewrite the explicit formula in function form. The identify the y-

intercept of the function.
an = 10+2(n-1)

Answer 1

The explicit formula an = 10+2(n-1) can be rewritten in function form as f(n) = 10 + 2(n - 1). The y-intercept of the function is 8, which is the value of the function when n is zero.

Step-by-step explanation:

To rewrite the explicit formula an = 10 + 2(n - 1) in function form, we start by replacing an with f(n), which yields:

f(n) = 10 + 2(n - 1).

This is the function in function notation. Now, to identify the y-intercept of the function, we need to find the value of f(n) when n is zero:

f(0) = 10 + 2(0 - 1) = 10 - 2 = 8.

The y-intercept of the function is 8. This is the point where the graph of the function will cross the y-axis when the function is graphed on a coordinate plane.

Answer 2

We have the relation:

aₙ = 10 + 2*(n - 1)

And we want to write this in fuction form:

y = f(n)

first we have:

aₙ = y = 10 + 2*(n - 1)

We can rewrite this as:

y = 10 + 2*n - 2

y = 2*n + (10 - 2)

y = 2*n + 8

Now we want to find the y-intercept, this is the value of the function when the variable is equal to zero.

Then if we take n = 0, we get:

y = 2*0 + 8

y = 8

The y-intercept is 8.