Question

The graph of f(x) = |x| is vertically stretched by a factor of 3, shifted left 2 units, shifted down 4 units and reflected over the x-axis. What is the function equation of the resulting graph?

Answer 1

Step-by-step explanation:

Step 1:  Add the vertical stretch

$f(x) = |x|$

$f(x) = 3|x|$

Step 2:  Shift it to the left 2 units

$f(x) = 3|x|$

$f(x) = 3|x + 2|$

Step 3:  Shift it down 4 units

$f(x) = 3|x + 2|$

$f(x) = 3|x + 2| - 4$

Step 4:  Reflect it across the x-axis

$f(x) = 3|x + 2| - 4$

$f(x) = -3|x + 2| - 4$

Answer:  $f(x) = -3|x + 2| - 4$

Answer 2

Answer:

The final transformed function becomes:

$f(x)=-3\,|x-2|+4$

Step-by-step explanation:

The first transformation (vertically stretched by a factor of 3) means we multiply by 3 the original function:

$f(x)= 3\,|x|$

second transformation (shifted left 2 units) means we add 2 units to "x":

$f(x)=3\,|x+2|$

third transformation (shifted down 4 units) implies that we subtract 4 units to the full functional expression:

$f(x)=3\,|x+2|-4$

fourth transformation (reflected over the x-axis) implies that we multiply the full functional expression by "-1":

$f(x)=(-1)\,(3\,|x+2|-4)\\f(x)=-3\,|x-2|+4$