Question

BCer3TW35Q/viewfo11. Graph the function. Label the vertex and axis of symmetry. State the domainand range. Then describe where the function is increasing and decreasing.f(x) = 2(x - 1)(x - 3)

Answer 1

$\begin{gathered} f(x)=2(x-1)(x-3) \\ f(x)=2(x^2-3x-x+3) \\ f(x)=2(x^2-4x+3) \\ f(x)=2x^2-8x+6 \\ x=1,\text{ }f(1)=2(1)^2^{}-8(1)+6=0 \\ x=2,f(2)=2(2)^2-8(2)+6=-2 \\ x=0,f(0)=2(0)^2-8(0)+6=6 \\ x=-1,f(-1)=2(-1)^2-8(-1)+6=16 \\ x=-2,f(-2)=2(-2)^2-8(-2)+6=30 \end{gathered}$

domain = {-2, -1, 0, 1, 2}

range = {30, 16, 6, 0, -2}

For a decreasing function y value decrease as x values increase. The value start decreasing at -2

For a increasing function y values increases as x values increase. The value start increasing at 2.