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# Suppose the graph of $f$ is given. Write equations for the graphs that are obtained from the graph of $f$ as follows.(a) Shift 3 units upward.(b) Shift 3 units downward.(c) Shift 3 units to the right.(d) Shift 3 units to the left.(e) Reflect about the x-axis.(f) Reflect about the y-axis.(g) Stretch vertically by a factor of 3.(h) Shrink vertically by a factor of 3.

## (a) If the graph of $f$ is shifted 3 units upward, its equation becomes $y=f(x)+3$.(b) If the graph of $f$ is shifted 3 units downward, its equation becomes $y=f(x)-3$.(c) If the graph of $f$ is shifted 3 units to the right, its equation becomes $y=f(x-3)$.(d) If the graph of $f$ is shifted 3 units to the left, its equation becomes $y=f(x+3)$.(e) If the graph of $f$ is reflected about the $x$ -axis, its equation becomes $y=-f(x)$.(f) If the graph of $f$ is reflected about the $y$ -axis, its equation becomes $y=f(-x)$.(g) If the graph of $f$ is stretched vertically by a factor of 3 , its equation becomes $y=3 f(x)$.(h) If the graph of $f$ is shrunk vertically by a factor of $3,$ its equation becomes $y=\frac{1}{3} f(x)$.

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