Instructions: For the function given, determine the direction and amount of horizontal shift from the original function y=(3)x𝑦=(3)𝑥.y=3x−5−3
Question
For the function given, determine the direction and amount of horizontal shift from the original function
y = (3)^{x}
Final transformed function:
y = 3^{x - 5} - 3
Solution
The given function is y = 3x - 5 - 3.
First, simplify the function by combining like terms. This gives us y = 3x - 8.
The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept. In this case, m = 3 and b = -8.
The horizontal shift of a function is determined by the value of b. If b is positive, the function shifts to the right. If b is negative, the function shifts to the left.
In this case, b = -8, so the function y = 3x - 8 shifts 8 units to the left from the original function y = 3x.
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