Question

Review the graph of f(x) = RootIndex 5 StartRoot x EndRoot and the graph of the transformed function g(x). On a coordinate plane, y = f (x) curves up through (negative 1, negative 1) to inflection point (0, 0), and then curves up through (1, 1). Y = g (x) curves down through (negative 5, 2) to inflection point (negative 4, 0), and then curves down through (negative 3, negative 2) and (4, negative 3). If g(x) = a · f(x + b), how is f(x) transformed to get g(x)? –2f(x + 4) –2f(x – 4) –f(x + 4) –f(x – 4)

Answer 1

Function transformation involves changing the form of a function.

f(x) is transformed to g(x) by (a) -2f(x + 4)

The function is given as:

$f(x) = \sqrt[5]{x}$

Start by shifting f(x) to the left by 4 units.

The rule of this transformation is:

$(x,y) \to (x + 4,y)$

So, we have:

$f(x + 4) = \sqrt[5]{x + 4}$

Next, the function is stretched by a factor of 2.

The rule of this transformation is:

$(x,y) \to (x,2y)$

So, we have:

$2f(x + 4) = 2\sqrt[5]{x + 4}$

Rewrite as:

$g(x) = 2\sqrt[5]{x + 4}$

The above function passes through the points (-5, 2), (-4, 0), (-3, -2) and (4, -3)

Hence, f(x) is transformed to g(x) by -2f(x + 4)

Read more about function transformation at:

https://brainly.com/question/1548871

Answer 2

Answer:

-2f(x + 4)

Step-by-step explanation:

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