Question

Given f(x) and g(x) = f(x + k), use the graph to determine the value of k. Two lines labeled f of x and g of x. Line f of x passes through points 0, 0 and 2, 2. Line g of x passes through points negative 4, 0 and negative 2, 2.

Answer 1

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Answer:

  k = 4

Step-by-step explanation:

The point (0, 0) on the graph of f(x) tells you f(0) = 0.

The point (-4, 0) on the graph of g(x) tells you g(-4) = 0.

Now we know that

  g(-4) = 0 = f(0) = f(-4+k)

or ...

  0 = -4 +k

  4 = k

The value of k is 4.

_____

f(x+k) shifts the graph of f(x) to the left k units. The points on the graph of g(x) all have x-values that are left of the corresponding f(x) points by 4 units. Hence k=4.

Answer 2

When a function is shifted in the vertical or horizontal direction, the function is translated.

The value of k is -4.

Given that:

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

For f(x), we have:

$(x,y) = \{(0,0),(2,2)\}$

For g(x), we have:

$(x,y) = \{(-4,0),(-2,2)\}$

$g(x) = f(x + k)$ means that:

$x_g = x_f + k$

From the ordered pair;

When x = 0 in f(x), the corresponding value of x in g(x) is -4.

This means that:

$x_g =-4$

$x_f = 0$

So, we have:

$x_g = x_f + k$

$-4 = 0 + k$

$-4 = k$

Rewrite as

$k = -4$

Hence, the value of k is -4.

Read more about translations at:

https://brainly.com/question/12463306