Question

Fill in each swing so that the resulting statement is true

Answer 1

Function transformation rule

f(bx) horizontally stretches f(x) when 0 < |b| < 1. The point (x, y) is transformed into (x/b, y)

In this case, the transformation is:

$f(\frac{1}{8}x)$

Considering the above rule:

$b=\frac{1}{8}$

which satisfy the criterium:

$\begin{gathered} 0<|\frac{1}{8}|<1 \\ 0<\frac{1}{8}<1 \end{gathered}$

The point (x,y) in f(x) is transformed in f(x/8) as follows:

$(x,y)\rightarrow(\frac{x}{\frac{1}{8}},y)\rightarrow(8x,y)$

In conclusion, the graph of y = f(x/8) is obtained by a horizontal stretch of the graph of y = f(x) by multiplying each of its x-coordinates by 8