Question

What transformation has changed the parent function f(x) = (.5)x to its new appearance shown in the graph below?

Answer 1

Answer:

Last option

−1 • f(x)

Step-by-step explanation:

The function $f(x) = (0.5) ^ x$ passes through point (-1, 2) because:

$f(-1) = (0.5) ^ {-1}= \frac{1}{(0.5)} = 2$

and also goes through the point (0, 1)

Because:

$f(0) = (0.5)^0 = 1$

Then, if the transformed function passes through the point (0, -1) and passes through the point (-1, -2) then this means that the graph of $f(x) = (0.5) ^ x$ reflected on the axis x. This means that if the point $(x_0, y_0)$ belongs to f(x), then the point $(x_0, -y_0)$ belongs to the transformed function

The transformation that reflects the graph of a function on the x-axis is.

$y = cf(x)$

Where c is a negative number. In this case $c = -1$

Then the transformation is:

$y = -1*f(x)$

and the transformed function is:

$f (x) = - (0.5) ^ x$

Observe the attached image.

Answer 2

Answer:

f(x) -2 is the correct answer.

Step-by-step explanation:

Just took the test!