Question

The function f(x) is shown on the provided graph. Graph the result of the following transformation on f(x).

Answer 1

Answer:

Observe the attached image

Step-by-step explanation:

We have the graph of a line that passes through the points (0,5) and (2, 1).

The equation of the line that passes through these points is found in the following way:

$y = mx + b$

Where

m = slope

$m = \frac {y_2-y_1}{x_2-x_1}\\\\m = \frac{1-5}{2-0}\\\\m = -2\\\\b = y_2-mx_2\\\\b = 1 -(-2)(2)\\\\b = 5$

So

$y = -2x + 5$

We must apply to this function the transformation$f (x-4)$.

We know that a transformation of the form

$y = f (x + h)$ shifts the graph of the function f(x) h units to the right if $h$, or shifts the function f(x) h units towards the left if $h> 0$.

In this case $h = -4$ then the transformation $f(x-4)$ displaces the graph 4 units to the right.

Therefore if f(x) passes through the points (0,5) and (2,1) then $f (x-4)$ passes through the points (4, 5) (6, 1)

And its equation is:

$y = -2(x-4) +5\\\\y = -2x +13$

Observe the attached image