Question

graph the following function on the axes provided. f(x)={-5 for -5 <= x < -1, 2x - 3 for -1 < x < 5} click and drag to make a line. click the line to delete it. click on an endpoint of a line to change it.

Explanation:

Step1: Analyze the first - piece function

For \(f(x)= - 5\) when \(-5\leq x<-1\). This is a horizontal line at \(y = - 5\). We find the two endpoints. When \(x=-5\), \(y = - 5\) (a closed - circle since \(x=-5\) is included in the domain \(-5\leq x<-1\)), and when \(x=-1\), \(y = - 5\) (an open - circle since \(x=-1\) is not included in the domain \(-5\leq x<-1\)).

Step2: Analyze the second - piece function

For \(f(x)=2x - 3\) when \(-1

Answer:

Graph a horizontal line \(y=-5\) from \(x=-5\) (closed - circle) to \(x=-1\) (open - circle) and then graph the line \(y = 2x - 3\) from \(x=-1\) (open - circle) to \(x = 5\) (open - circle).