what is the function rule for the transformed with vertical stretch by a factor of 2 and translated down 6

1 answer:

5 0

Answer: Thus, the equation of a function stretched vertically by a factor of 2 and then shifted 3 units up is y = 2f (x) + 6, and the equation of a function stretched horizontally by a factor of 2 and then shifted 6 units left is y = f ( (x - 6)) = f ( x - ). Example: f (x) = 2x2.

Step-by-step explanation:

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4/10x - 2x + 8/5 = 4/5

mamaluj [8]

$\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}$

Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.

$\large\displaystyle\text{$\begin{gathered}\sf \frac{2}{5}x-2x+\frac{8}{5}=\frac{4}{5} \end{gathered}$}$

Combine $\bf{\frac{2}{5}x }$ and -2x to get $\bf{-\frac{8}{5}x}$ .

$\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x+\frac{8}{5}=\frac{4}{5} \ \end{gathered}$}$

Subtract 8/5 from both sides.

$\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}$

Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.

$\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}$

Subtract 8 from 4 to get -4.

$\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=-\frac{4}{5} \end{gathered}$}$

Multiply both sides by $\bf{-\frac{5}{8}}$ , the reciprocal of $\bf{-\frac{5}{8}}$ .

$\large\displaystyle\text{$\begin{gathered}\sf x=-\frac{4}{5}\left(-\frac{5}{8}\right) \end{gathered}$}$

Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

$\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}$
$\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}$