Suppose g(x) = f(x) + k. Identify a value of k that transforms f into g.

The transformation that maps f into g is a translation transformation,

involving the addition of k to the value of f(x).

Reasons:

Points on the graph of g(x) are; (0, -3) and (0, 1)

The equation of g(x) is; y - (-3) = 4·x, which gives;

y = 4·x - 3

The y-intercept = -3

Points on the graph of f(x) are; (-1 -2) and (0, 2)

The equation of f(x) is; y - (-2) = 4·(x - (-1)), which gives;

y = 4·x + 4 - 2 = 4·x + 2

The y-intercept = 2

The slopes of the graphs of f(x) and g(x) are equal, therefore, f(x) ║ g(x)

The difference or the transformation that takes the y-intercept of f(x) to the

y-intercept of g(x) is; k = y-intercept(g(x)) - y-intercept(f(x)) = -3 - 2 = -5

Therefore, k = -5

Which gives;

g(x) = f(x) - 5

The value of k that transforms f into g is; k = -5

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Step-by-step explanation:

Given

Required

Determine the value of k

First, we need to determine the equation of g(x)

Start by calculating the slope (m)

Where x and y are two corresponding values:

The slope (m) is:

The equation is calculated using:

Where

and

Make y the subject of formula

So:

Next, we determine the equation of f(x)

Start by calculating the slope (m)

Where x and y are two corresponding values:

The slope (m) is:

The equation is calculated using:

Where

and

Make y the subject of formula

So:

Recall that

Make k the subject

Substitute values for g(x) and f(x)

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