what are the c-intercepts of the piecewise eaqution;

Question

y= x-2 if x<3 

y=-2+7 if x≥3

Answer 1

This question has two problems.

1.  y = x -2  ------------(1) this is ok.

    y = -2 + 7 -----------(2) this equation seems y = -x +7  (may be)

2. the domains of equation (1) and equation (2) are totally separated therefore, there is no common domain sets.

   So, there should be no cross intercepts for any fuctions of equations.

if there are no limitations for equation (1) and (2) for x values such as -∞ < x < ∞ then there is  a cross intercept for equation (1) and (2).

3. If I assum, there is no limitation for x value (i.e. domain) and given equations are

    y = x - 2 for all x values        ------------------(1)'

    y = -x + 7 for all x values     -------------------(2)'

The equation (1)' and equation (2)' are work with the same variable x and y.

Let y variable is the same for equation (1)' and (2)', then

  x -2 = -x +7  → 2x = 9  so, x = 9/2  plug in this x value to equation (1)' then

        y = 9/2 -2 = 5/2 

the cross intercept of two equations is (9/2, 5/2).

I hope this will help you.