Given f(x)=2^x and g(x)= f(x-3)+4, write the new function rule (equation) for function g and describe (using words) the two transformations that occur between the function f and the function g

*Some good words to consider using would include horizontal, vertical, stretch, compression,
translation, reflection, and phrases such as “to the left”, “to the right”, “up”, “down”, “by a
factor of__, or ”over the __ axis”.

Answer:

Just like Transformations in Geometry, we can move and resize the graphs of functions. Let us start with a function, in this case it is f(x) = x2, but it could be anything: ... g(x) = x2 + C. Note: to move the ... If you change that to (age+4) = 25 then you will get it when you are 21. Adding 4 ... Example: the function v(x) = x3 - x2 + 4x.

Step-by-step explanation:

The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s). For example -

y = 4x⁴ + 3x³ + 2x² + 6x + 7

We have the following polynomial functions -

f(x) = 2ˣ

g(x) = f(x - 3) + 4

We can write g(x) as -

g(x) = 2ˣ ⁻ ³ + 4 = (2ˣ/2³) + 4

g(x) = (2ˣ/8) + 4

The graph of f(x) is stretched by the factor of 1/8 and is shifted 4 units upwards.

Therefore, the graph of f(x) is stretched by the factor of 1/8 and is shifted 4 units upwards to given the function g(x)

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