Question

The graph of a function is shown.y-5-3-25.04-32+T№-2+-37912 345 xWhich function is represented by the graph?x - 3, x < 0O f(x)=3,x 20x + 3, x < 0f(x) = = (3.13,XO0 = (3x²-x+ 3, x≤ 03,x > 0-x-3, x≤0>= (3x3,x > 0O f(x) =O f(x) =

Answer 1

`f(x)=\begin{cases}x+3\text{ }x{<0} \\ {3}\text{ }x\ge0\end{cases}`

Explanations:

The given graph is made of 2 lines including a horizontal line.This functions are referred to as piecewise function

The given horizontal line will be expressed as y = b where b is the y-intercept of the line. Since the horizontal line pass through the coordinate (0, 3), hence the equation of the horizontal line is y = 3

For the other function, we will find the equation of a line passing through the coordinates (-3, 0) and (-2, 1)

Find the slope

`\begin{gathered} Slope=(1-0)/(-2-(-3)) \\ Slope=(1)/(-2+3) \\ Slope=1 \end{gathered}`

The y-intercept is (0, 3). The equation of the other line will be y = x + 3

The piecewise function represented by the graph is given as:

`f(x)=\begin{cases}x+3\text{ }x{<0} \\ {3}\text{ }x\ge0\end{cases}`