Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Analyze a transformed exponential graph from a,b,h,k
Problem
Analyze \(y~=~2^{x~-~3}~+~4\) relative to \(y~=~2^x\). State the base and transformations, map parent point \((0,~1)\), and give the asymptote and range.
Compare the moved key point and the shifted baseline.Open full size
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What this problem is really about
An exponential transformation is easiest to track through its baseline and the parent anchor where the exponent is zero. Move that anchor according to the horizontal and vertical shifts, then move the horizontal asymptote by the outside shift alone. Because the exponential part stays positive, its sign relative to the new baseline determines the range side.
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