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If f(x)=2^x is the parent function, and a transformation tales place to create g(x)=2^x-3, describe the transformation

a) the function shifted left 3 units
b) the function moved down 3 units
c) the function was reflected over the y-axis
d) the function moved up 3 units

If f(x)=2^x is the parent function, and a transformation tales place to create g(x-example-1
User Pypae
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The transformation is a downward vertical shift of 3 units. g(x) takes each output value of f(x) and subtracts 3, effectively moving the graph down 3 units without changing its shape.

Option B is correct.

The correct answer is: b) the function moved down 3 units.

Here's why:

Shifting a function left or right involves changing the input (x-value) by a constant amount. In this case, g(x) doesn't have a shifted input term compared to f(x).

Reflecting a function over the y-axis negates its output values. For example, if f(x) = 2, then g(x) would be -2. However, here, both functions have the same output values for the same input values.

Moving a function up or down involves adding or subtracting a constant value to its output. In this case, g(x) = f(x) - 3, which means every output value of f(x) is reduced by 3 to obtain the corresponding output value of g(x). Therefore, the function is shifted down 3 units.

So, the transformation that takes f(x) to g(x) is a vertical shift downwards by 3 units.

User Matthew Coelho
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