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# function question

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Suppose a function f(x) has domain (-inf,inf) and range [-11,3]. If we define a new function by

g(x) = 6f(x/2) + 1

then what is the range of g(x)? Express your answer in interval notation.

May 23, 2021

$$f(\frac{x}{2})$$has the same range as f(x) since the function is stretched by a factor of 2 horizontally and y values are not affected. $$6f(\frac{x}{2})$$, however, has range [6(-11), 6(3)]=[-66, 18], since we are stretching the graph in the y directions by a factor of 6. Finally, we shift the graph up by one unit to get $$6f(\frac{x}{2})+1$$ and that transformation changes the range to [-65, 19].