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?

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mberisso mberisso · Answer 1 · 2020-05-21T20:05:33+02:00

Answer:

The final transformed function becomes:

[tex]f(x)=-3\,|x-2|+4[/tex]

Step-by-step explanation:

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

[tex]f(x)= 3\,|x|[/tex]

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

[tex]f(x)=3\,|x+2|[/tex]

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

[tex]f(x)=3\,|x+2|-4[/tex]

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

[tex]f(x)=(-1)\,(3\,|x+2|-4)\\f(x)=-3\,|x-2|+4[/tex]

igoroleshko156 igoroleshko156 · Answer 2 · 2020-05-21T20:51:15+02:00

Step-by-step explanation:

Step 1: Add the vertical stretch

[tex]f(x) = |x|[/tex]

[tex]f(x) = 3|x|[/tex]

Step 2: Shift it to the left 2 units

[tex]f(x) = 3|x|[/tex]

[tex]f(x) = 3|x + 2|[/tex]

Step 3: Shift it down 4 units

[tex]f(x) = 3|x + 2|[/tex]

[tex]f(x) = 3|x + 2| - 4[/tex]

Step 4: Reflect it across the x-axis

[tex]f(x) = 3|x + 2| - 4[/tex]

[tex]f(x) = -3|x + 2| - 4[/tex]

Answer: [tex]f(x) = -3|x + 2| - 4[/tex]

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