Question

need help with these parts. both parts use the same table

Answer 1

Given:

$f(x)=h(2x)$

And the values in the table.

Required:

The equation of a normal line to f at x=3.

Explanation:

The equation of the line that passes through from point (x,y) and has slope m

is given by the formula

$y-y_1=m(x-x_1)$

From the table at x=3, f(x)=h(2x)

that is f(3)= h(6)=9

And the slope from the table at x=3 is 1/2.

Now the equation of the line is:

$\begin{gathered} y-9=\frac{1}{2}(x-3) \\ 2(y-9)=(x-3) \\ 2y-18=x-3 \\ x-2y=-15 \end{gathered}$

Final answer:

Thus the equation of the normal line is

$x-2y+15=0$