Question

100 points
which of the following is the graph of the piecewise function

Answer 1

A piecewise function is a function that is defined by different formulas for different parts of its domain. The domain is the set of all possible input values for the function.

The graph is plotted on a Cartesian plane with x and y axes. The x-axis is the horizontal line that shows the input values of the function, and the y-axis is the vertical line that shows the output values of the function. The graph is drawn with a scale of one unit per grid line.

Answer 2

A

Explanation:

Look at the last part of the definition.

y = log(base 2) (x + 1)

log(base 2) 2 = 1

When x = 1, y = log(base 2) (1 + 1) = log(base 2) 2 = 1

The point (1, 1) is in the function.

Graphs 2 and 3 are eliminated.

In graphs 1 and 4, the parts with x ≤ -2 are the same. Also, the parts

with x ≥ 1 are also the same.

We need to look in the middle section of graphs 1 and 4 to see which one of the two is the graph of the function.

Look at x = -1 and

y = -x/(x² + x - 2)

y = 1/(1 - 1 - 2) = -0.5

The middle part of the graph of the first choice does include point (-1, -0.5), and graph 4 does not include it.

Answer: A