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The graph of the absolute value parent function, f(x) = |x|, is stretched horizontally by a factor of 3 to create the graph of g(x). What function is g(x)? O A. g(x) = |3x| O B. g(x) = |x+3| O C. g(x) = 3|x| O D. g(x) = |1/3x|​

Respuesta :

abidemiokin

Answer:

B. g(x) = |x+3|

Step-by-step explanation:

If the graph of the absolute value parent function, f(x) = |x|, is stretched horizontally by a factor of 3 to create a graph of g(x), stretching horizontally by a factor means there is an increase in the parent function g(x) by 3. Hence the resulting function of g(x) will be the function of x plus the unit value of 3 as shown;

Given f(x) = |x|, if f(x) is stretched by 3 to produce g(x) then;

g(x) = f(x+3)

f(x+3) is gotten by replacing x in the function f(x) by x+3.

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

Since g(x) = f(x+3) as shown above, therefore;

g(x) = |x+3|

Therefore the correct option is B i.e g(x) = |x+3|

MrRoyal

Answer:

[tex]g(x) = |x - 3|[/tex]

Step-by-step explanation:

Given

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

Stretched horizontally by 3

Required

Determine g(x)

When a graph is translated horizontally, we have:

[tex]g(x) = f(x - h)[/tex]

Where h is the unit translated

In this case;

[tex]h = 3[/tex]

So:

[tex]g(x) = f(x -3)[/tex]

Solving f(x-3)

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

Hence;

[tex]g(x) = |x - 3|[/tex]

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