Question

Graph the function, in the answer box, describe the function please?

Answer 1

piecewise linear continuous

Explanation:

up to `x = -4` - but not at this point - the graph is drawn with the line `y = -3(x+6)`, or `y = -3x - 18`.

the `x`-intercept of this line is `(-6, 0)`. there is no `y`-intercept for this line, since it does not include a point where `x=0`.

at `x = -4`, and to the right of this. the graph is drawn with the line `y = 0.5(x-8)`, or `y = 0.5x - 4`.

the `x`-intercept of this line is `(8.0)`, and the `y`-intercept is `(0, -4)`.

the function is piecewise since it is defined by multiple sub-functions (in this case, 2).

in order to evaluate a piecewise function for a given value of `x`, the appropriate subdomain (e.g. `x<-4`) needs to be chosen.

this means that the correct function `f(x)` can be selected, to produce the correct `y`-value.

it is linear since it is composed of straight-line sections.

it is continuous since both functions that define it are also continuous, and there is no discontinuity at the endpoints of each one. (`x=-4` is defined here, using `y = 0.5(x-8)`.)