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)? On a coordinate plane, a piecewise function has 2 lines. The first line goes through (negative 3, 4) and goes down to a closed circle at (negative 1, 0). The second line has a closed circle at (1, 0) and goes up through (3, 4). On a coordinate plane, a piecewise function has 2 lines. The first line goes up through (negative 3, negative 4) to a closed circle at (0, 2). The second line has a closed circle at (0, 2) and goes down through (3, negative 4). On a coordinate plane, a piecewise function has 2 lines. The first line goes up from (negative 2, negative 5) to a closed circle at (0, negative 1). The second line has a closed circle at (0, 1) and goes down through (2, negative 3). On a coordinate plane, a piecewise function has 2 lines. The first line goes down through (negative 1, 3) to a closed circle at (0, 1). The second line has a closed circle at (0, negative 1) and goes up through (2, 3).

Answer 1

Answer:

1.- negative

2.+positive

Answer 2

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:

The graph exists a straight line that starts with an open circle at $f(x) = +1$ and slopes downwards from left to right.

Step-by-step explanation:

Given:

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

The given piecewise function is presented as follows;

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

Find:

To find the graph of f(x)

Step 1

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

Step 2

At $x = 0, f(x) = 0$

which represents a point on the graph

For $x > 0, f(x) = -2*x + 1$

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

The slope of the graph, $m = -2$

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

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