Question

find the value of k that transforms the graph of f(x) into graph g. then describe the transformation.
10 ( g(x) = f(x) + k )
11 ( g(x) = f(x) + k )
12 ( g(x) = f(x - k) )
13 ( g(x) = f(x - k) )
14 ( g(x) = kf(x) )
15 ( g(x) = f(kx) )

Explanation:

Let's solve problem 10 as an example (since the user didn't specify, we'll pick one).

Problem 10: \( g(x) = f(x) + k \)

We need to find \( k \) and describe the transformation.

Step 1: Identify a point on \( f(x) \) and \( g(x) \)

Let's take a point on \( f(x) \), say when \( x = 2 \), from the graph, \( f(2) \) seems to be 3 (assuming grid values). A corresponding point on \( g(x) \), when \( x = 2 \), let's say \( g(2) \) is 1 (from the graph).

Step 2: Use the equation \( g(x) = f(x) + k \)

Substitute \( x = 2 \) into \( g(x) = f(x) + k \):
\( g(2) = f(2) + k \)
We have \( g(2) = 1 \) and \( f(2) = 3 \), so:
\( 1 = 3 + k \)

Step 3: Solve for \( k \)

Subtract 3 from both sides:
\( k = 1 - 3 = -2 \)

Step 4: Describe the transformation

The equation \( g(x) = f(x) + k \) with \( k = -2 \) means \( g(x) = f(x) - 2 \). This is a vertical shift down by 2 units.

Answer:

The value of \( k \) is \( -2 \), and the transformation is a vertical shift of the graph of \( f(x) \) down by 2 units.