Given f(x) and g(x) = f(x + k), use the graph to determine the value of k.

a.) -4
b.) -2
c.) 2
d.) 4

4

Step-by-step explanation:

Notice at say x=-4, that the y-coordinate for the function g is 0 so g(-4)=0.

Now notice the same y-coordinate is obtained when x=0 for function, f, so f(0)=0.

So g(-4)=f(0) which means g(-4)=f(-4+4).

This implies k is 4.

Let's try it for another x.

For y=-1, we see this happens at x=-5 for g and at x=-1 for f.

So does g(x)=f(x+4) hold for x=-5.

Plug in -5 for x:

g(-5)=f(-5+4)

-1=f(-1)

-1=-1

Also if you look at g it is just a translation of f 4 units left of where f is.

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

step-by-step explanation:

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