Function transformation involves changing the form of a function.
The graphs of f and their transformations g are:
- Graph 1: f(x) = 2^x, g(x) = f(x) + k where k = 2
- Graph 2: f(x) = 2^x, g(x) = f(x + k) where k = -2
- Graph 3: f(x) = 0.5^x, g(x) = f(x) + k where k = 2
- Graph 4: f(x) = 0.5^x, g(x) = f(x + k) where k = -2
How to determine the graphs and their transformation
From the graphs, the graphs of f(x) that represent [tex]f(x) = 2^x[/tex] are graph 1 and graph 2.
In graph 1, function f(x) is shifted up by 2 units to form g(x), while f(x) is shifted right by 2 units to form g(x) in graph 2
So, the equations of graphs 1 and 2 are:
- Graph 1: f(x) = 2^x, g(x) = f(x) + k where k = 2
- Graph 2: f(x) = 2^x, g(x) = f(x + k) where k = -2
Similarly, the graphs 3 and 4 represent [tex]f(x) = 0.5^x[/tex] for f(x)
In graph 3, function f(x) is shifted up by 2 units to get g(x), while f(x) is shifted right by 2 units to form g(x) in graph 4
So, the equations of graphs 3 and 4 are:
- Graph 3: f(x) = 0.5^x, g(x) = f(x) + k where k = 2
- Graph 4: f(x) = 0.5^x, g(x) = f(x + k) where k = -2
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