The function f(x)=x−−√ is reflected over the x-axis, translated 4 units down and 5 units to the left, then vertically stretched

Question

3 years ago

12

by a factor of 3. Which equation best represents the new function created?

2 answers:

Gnesinka [82] · Answer 1 · 2022-09-02T13:26:27+03:00

Transformation involves changing the position of a function.

The equation of the new function is: $\mathbf{g(x) = -3\sqrt{x + 5} - 12}$

The function is given as:

$\mathbf{f(x) = \sqrt x}$

The rule of reflection across the x-axis is:

$\mathbf{(x,y) \to (x,-y)}$

So, we have:

$\mathbf{f'(x) = -\sqrt x}$

The rule of translation, <em>4 units down and 5 units left </em>is:

$\mathbf{(x,y) \to ( x + 5,y-4)}$

So, we have:

$\mathbf{f"(x) = -\sqrt{x + 5} - 4}$

The rule of vertical stretch by a factor of # is:

$\mathbf{(x,y) \to (x,3y)}$

So, we have:

$\mathbf{g(x) = 3(-\sqrt{x + 5} - 4)}$

$\mathbf{g(x) = -3\sqrt{x + 5} - 12}$

Hence, the equation of the new function is:

$\mathbf{g(x) = -3\sqrt{x + 5} - 12}$