Question

The graph is a transformation of one of the basic functions. Find the equation that defines the function.

Answer 1

Answer:

$y = 5-\sqrt{x}$

Step-by-step explanation:

Note that the graph shown is a transformation of the parent function

$y = \sqrt{x}$

The main function cuts the x-axis at x = 0 and has no negative values of y. In addition, the main function is always growing.

Note that the function shown is decreasing and intercepts the y-axis at y = 5.

Therefore, the graph of the main function has been reflected on the x-axis and displaced 5 units upwards.

If we do y = f(x) then to reflect the main function on the  x-axis and move it upwards 5 units we make the following transformation

$y = -f(x) + 5$.

Then the graphed function is:

$y = 5-\sqrt{x}$

Answer 2

Answer:

f(x) = -logx + 4.

Step-by-step explanation:

y = -log x  approaches  the point (0, 1)  but this approaches (0, 5)

Looks like the graph of - log x + 4.