express the function graphed on the axes below as a piecewise function.\nanswer attempt 1 out of 3\n$f(x) =…

express the function graphed on the axes below as a piecewise function.\nanswer attempt 1 out of 3\n$f(x) = \\begin{cases}\n\\square \\text{ for } \\square \\\\\n\\square \\text{ for } \\square\n\\end{cases}$

express the function graphed on the axes below as a piecewise function.\nanswer attempt 1 out of 3\n$f(x) = \\begin{cases}\n\\square \\text{ for } \\square \\\\\n\\square \\text{ for } \\square\n\\end{cases}$

Answer

Explanation:

Step1: Analyze the left line

The left line passes through ((-8, 0)) and ((-4, 5)). The slope (m_1=\frac{5 - 0}{-4 - (-8)}=\frac{5}{4}). Using point - slope form (y - y_1=m(x - x_1)) with ((x_1,y_1)=(-8,0)), we get (y-0=\frac{5}{4}(x + 8)), which simplifies to (y=\frac{5}{4}x + 10). The domain of this line is (x\lt - 4) (since there is an open circle at (x=-4)).

Step2: Analyze the right line

The right line passes through ((2, 6)) and ((8, 0)). The slope (m_2=\frac{0 - 6}{8 - 2}=\frac{-6}{6}=-1). Using point - slope form (y - y_1=m(x - x_1)) with ((x_1,y_1)=(2,6)), we get (y - 6=-1(x - 2)), which simplifies to (y=-x + 8). The domain of this line is (x\gt2) (since there is an open circle at (x = 2)).

Answer:

(f(x)=\begin{cases}\frac{5}{4}x + 10& \text{for }x\lt - 4\-x + 8& \text{for }x\gt2\end{cases})