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) $y=8-2x^2$. (c) $y=e^{-2x-8}$. (d) $y=\lg x,\ x>0$.

Transformations of Graphs - Translations, Reflections and Scalings of Graphs

Transformations of Graphs - Translations, Reflections and Scalings of Graphs

Solution:

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