Question

Solve for the y-intercept of the second piece of the piecewise function F(x): F(x) = 3 + 0.6(x - 0), Y2 + 0.8(x - 3) (Note that the y-intercept b₂ is not equivalent to the value of Y2.)

a) b₂ = 4.8
b) b₂ = 3
c) b₂ = 0.6
d) b₂ = 2.4

Answer 1

b₂ = 0.6, The y-intercept (b₂) of the second piece of the piecewise function is found to be 0.6 when evaluating the function at x = 0.

Thus option c is correct.

Step-by-step explanation:

The y-intercept of a function is the point where the graph intersects the y-axis (where x = 0). In the given piecewise function F(x), the second piece of the function is F(x) = 0.8(x - 3) + Y2. To find the y-intercept (b₂) of this piece, we substitute x = 0 into the equation.

F(x) = 0.8(x - 3) + Y2

When x = 0,

F(0) = 0.8(0 - 3) + Y2

F(0) = 0.8(-3) + Y2

F(0) = -2.4 + Y2

For the y-intercept, x = 0, therefore:

F(0) = b₂

b₂ = -2.4 + Y2

We're given that Y2 = 3 in the piecewise function, so substituting Y2 = 3 into the equation:

b₂ = -2.4 + 3

b₂ = 0.6

Hence, the y-intercept (b₂) of the second piece of the piecewise function is 0.6.

This calculation determines the specific value of b₂ by evaluating the function at x = 0 to find where it intersects the y-axis. Substituting x = 0 into the equation and replacing Y2 with its given value, the calculation simplifies to find the value of b₂ as 0.6. This confirms the y-coordinate where the graph crosses the y-axis for the second piece of the function F(x).

Thus option c is correct.