Functions Answers: 7-6 Skills Practice Transformations Of Exponential

Then, the transformed function will look like this: [ g(x) = a \cdot b^(x-h) + k ] | Parameter | Effect on the graph | How it changes the equation/points | | :--- | :--- | :--- | | a (Vertical stretch/shrink & reflection) | - If |a| > 1: vertical stretch - If 0 < |a| < 1: vertical shrink - If a is negative : reflection over x-axis | Multiply all y-values by a. The y-intercept changes from 1 to a. | | h (Horizontal shift) | - Right if h > 0 - Left if h < 0 | Replace x with (x – h). The horizontal asymptote does NOT change. | | k (Vertical shift) | - Up if k > 0 - Down if k < 0 | Add k to the whole function. The horizontal asymptote changes from y=0 to y=k. | | b (Base) | - If b > 1: growth (increasing) - If 0 < b < 1: decay (decreasing) | Changes the steepness but not the asymptote. | Step-by-Step to Find the Answer for Any Problem Let’s say a problem gives you: ( y = 3 \cdot 2^(x-4) + 1 )

Set ( y = 0 ): ( 0 = 3 \cdot 2^(x-4) + 1 ) → ( -1 = 3 \cdot 2^(x-4) ) → ( -\frac13 = 2^(x-4) ). Since a positive base (2) to any power is always positive, there is no x-intercept . Then, the transformed function will look like this:

It’s ( y = k ). Here, ( k = 1 ). So the asymptote is ( y = 1 ). The horizontal asymptote does NOT change