Find and simplify the equation of the graph obtained when the graph of $y = 2x + 4$ is translated

Question

Find and simplify the equation of the graph obtained when the graph of $y = 2x + 4$ is translated by $3$ units in the positive $y$-direction, parallel to the $y$-axis, the graph of $y = 4 - x^2$ is scaled by a factor of $2$ parallel to the $y$-axis, the graph of $y = e^{-2x}$ is translated by $4$ units in the negative $x$-direction, parallel to the $x$-axis, the graph of $y = \lg\left(\frac{1}{x}\right)$ is reflected in the $x$-axis.

Accepted Answer

(a) $y=2x+7$ (b) $y=2\left( 4-{{x}^{2}} \right)$ (c) $y={{\operatorname{e}}^{-2\left( x+4 \right)}}$ (d) $y=\lg x$

Transformations of Graphs

Transformations of Graphs