Question

If f(3)=7 and f(1)=5, what is the function of f(x)?

Answer 1

f(3)=7 and f(1)=5, is just another way to say x = 3 and y = 7, as well as x = 1 and y = 5, which gives us the points of (3,7) and (1,5), so let's use them,

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 3 &,& 7~) % (c,d) &&(~ 1 &,& 5~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-7}{1-3}\implies \cfrac{-2}{-2}\implies 1 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-7=1(x-3) \\\\\\ y-7=x-3\implies y=x+4$