Question

The graph of a function is shown. On a coordinate plane, a function has 2 connecting line. The first line goes from (negative 5, negative 2) to (0, 3). The second line starts at (0, 3) and continues horizontally at y = 3. Which function is represented by the graph? f(x) = StartLayout enlarged left-brace 1st Row 1st column x minus 3, 2nd column x less-than 0 2nd Row 1st column 3, 2nd column x greater-than-or-equal-to 0 EndLayout f(x) = StartLayout enlarged left-brace 1st Row 1st column x + 3, 2nd column x less-than 0 2nd Row 1st column 3, 2nd column x greater-than-or-equal-to 0 EndLayout f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x + 3, 2nd column x less-than-or-equal-to 0 2nd Row 1st column 3, 2nd column x greater-than 0 EndLayout f(x) = StartLayout enlarged left-brace 1st Row 1st column negative x minus 3, 2nd column x less-than-or-equal-to 0 2nd Row 1st column 3, 2nd column x greater-than 0 EndLayout

Answer 1

Answer:

$f(x)=\left\{\begin{array}{l}x+3,\ \ x< 0\\ \\3,\ \ x\ge 0\end{array}\right.$

Step-by-step explanation:

The graph of a function is shown in attached diagram.

1. Write the equation of the left part. This is the straight line with the slope of

$\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-3}{-5-0}=\dfrac{-5}{-5}=1$

So, the equation of the line is

$y=1\cdot x+b\\ \\y=x+b,$

where b is the y-intercept.

This graph intersects the y-axis at point (0,3), so b = 3.

Therefore,

$y=x+3$

2. The equation of the right part is y = 3.

3. The expression for the function represented by the graph is

$f(x)=\left\{\begin{array}{l}x+3,\ \ x< 0\\ \\3,\ \ x\ge 0\end{array}\right.$

Answer 2

Answer:

A

Step-by-step explanation: