Question

What value of `a` would make the function `h(x)={x^3+a^3` if `x<2` and `4-2x` if `x>=2` continuous?

Answer 1

The y-coordinate at `x = 2` is `4 - 2(2) = 0`.

For the function to be continuous, we need to have the same y-value as above at the point where the piece wise functions are closest in terms of x-values.

`x^3 + a^3 = 0`

When `x = 2`:

`8 + a^3 = 0`

`a^3 = -8`

`a = -2`

If you were to graph the two piece-wis functions, you would find that they are indeed continuous.

Hopefully this helps!