Question

The piecewise function f(x) has opposite expressions. F(x) = startlayout enlarged left-brace 1st row 1st column 2 x minus 1, 2nd column x less-than 0 2nd row 1st column 0, 2nd column x = 0 3rd row 1st column negative 2 x + 1, 2nd column x greater-than 0 which is the graph of f(x)?.

Answer 1

The piecewise expression presented in the question gives values of f(x)

that change based on the range of the input value, x.

• The graph of the piecewise expression f(x) is attached

Reasons:

The given piecewise function is presented as follows;

• $f(x) = \begin{cases}2 \cdot x - 1, & \text{ if } x < 0 \\0, & \text{ if } x = 0\\-2 \cdot x + 1, & \text{ if } x > 0 \end{cases}$

Required:

To find the graph of f(x)

Solution:

From the piecewise function, we have;

• For x < 0, f(x) = 2·x - 1

The slope, m = 2

Therefore, as x tends to 0, f(x) tends to 2×0 - 1 = -1

Therefore, for x < 0, the graph starts with an open circle at f(x) = -1, and f(x) decreases as graph moves from right to left.

• At x = 0, f(x) = 0, which represent a point on the graph

• For x > 0, f(x) = -2·x + 1

Which gives that as x tends to 0, f(x) tends to +1

The slope of the graph, m = -2

Therefore, the graph is a straight line that starts with an open circle at f(x) = +1 and slopes downwards from left to right.

Please find attached the graph of f(x) created with MS Excel

Learn more about piecewise function here:

brainly.com/question/7352615

Answer 2

Answer:

C

Explanation:

took the test on edge :p