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|

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|

Step-by-step explanation:

Given

Stretched horizontally by 3

Required

Determine g(x)

When a graph is translated horizontally, we have:

Where h is the unit translated

In this case;

So:

Solving f(x-3)

Hence;

answer: it's d

step-by-step explanation:

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2