Question

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

Answer 1

Answer:

$k = 5$

Step-by-step explanation:

Given

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

Required

Determine the value of k

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

Start by calculating the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where x and y are two corresponding values:

$(x_1,y_1) = (1,1)$

$(x_2,y_2) = (0,-3)$

The slope (m) is:

$m = \frac{-3- 1}{0 - 1}$

$m = \frac{-4}{- 1}$

$m = 4$

The equation is calculated using:

$y - y_1 = m(x - x_1)$

Where

$m = 4$ and $(x_1,y_1) = (1,1)$

$y - 1 = 4(x - 1)$

$y - 1 = 4x - 4$

Make y the subject of formula

$y = 4x - 4 + 1$

$y = 4x - 3$

So:

$f(x) = 4x - 3$

Next, we determine the equation of f(x)

Start by calculating the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where x and y are two corresponding values:

$(x_1,y_1) = (-1,-2)$

$(x_2,y_2) = (0,2)$

The slope (m) is:

$m = \frac{2- (-2)}{0 - (-1)}$

$m = \frac{2+2}{0+1}$

$m = \frac{4}{1}$

$m = 4$

The equation is calculated using:

$y - y_1 = m(x - x_1)$

Where

$m = 4$ and $(x_1,y_1) = (-1,-2)$

$y - (-2) = 4(x - (-1))$

$y + 2 = 4(x +1)$

$y + 2 = 4x +4$

Make y the subject of formula

$y = 4x + 4 - 2$

$y = 4x + 2$

So:

$g(x) = 4x + 2$

Recall that

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

Make k the subject

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

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

$k = 4x + 2 - (4x - 3)$

$k = 4x + 2 - 4x + 3$

$k = 4x - 4x+ 2 + 3$

$k = 5$