Question

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

Answer 1

f(x) = -logx + 4.

Explanation:

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

Looks like the graph of - log x + 4.

Answer 2

`y = 5-√(x)`

Explanation:

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

`y = √(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-√(x)`