9514 1404 393
Answer:
see attached
Step-by-step explanation:
The graph shown with your problem statement does not pass the vertical line test, so is not the graph of a function. (A vertical line intersects the graph in more than one place.) This graph can be rejected immediately.
I find it convenient to look at the domain statements (x≤1 and x>1). This tells you that you can separately evaluate the graph to the left of x=1 and to the right of x=1. Each of those portions of the graph must match the corresponding expression.
Here, it looks sufficient to identify the slope of the line in each domain. (We don't know what graphs you're selecting from, so we don't know what you will need to look at to differentiate the correct one from the rest.)
For x < 1, the coefficient of x is 3, so the line will have a steep upward slope.
For x > 1, the coefficient of x is -2, so the line will have a slightly less steep downward slope.
The value of z(1) is 3(1)-2=1, so (1, 1) is at the top end of the line forming the left side of the graph. The limit as x approaches 1 from the right is -2(1)+3=1. This means the two lines meet at the point (1, 1) and the graph has a generally ∧ shape. The attachment shows the graph you're looking for.
