Question

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

Answer 1

4

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.

Answer 2

d) 4

Explanation:

Looking at the graph of f(x) we can see the following points:

`...(-1,-1),(0,0),(1,1),(2,2),(3,3)...` As the line crosses the origin the parameter "b"=0 therefore the rule of this function is y=x.

`f(x)=x`

As for
`g(x)`

1. Clearly g(x) is a translation of f(x) as

`g(x)=f(x+k)`

2. Since g(x) crosses the y-axis at (0,4) and

`\\g(x)=f(x+k)\\g(x)=f(x+4)`

g(x) can also be written as:

`g(x)=x+4`

3) Testing

Picking some points.

`g(x)=f(x+4)\Rightarrow g(0)=f(4)\\g(4)=f(x+4)\\g(4)=f(4+4) \Rightarrow g(4)=f(8)`

K then is 4 units.