Question

Don’t really know what linear functions are

Answer 1

Answer:

The rate of change of f(x) is greater than that of g(x)

They have the same y intercept of 14

Step-by-step explanation:

Given

$g(x) = -\frac{1}{2}x + 14$

Table for function f(x)

Required

Compare their rate of change and intercept

For g(x), we have:

$g(x) = -\frac{1}{2}x + 14$

The form of an equation is:

$y = mx + b$

Where

$m = slope$

$b =y\ intercept$

So:

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

$b = 14$

For f(x): Start by calculating the slope (m)

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

$m = \frac{17-16}{6-4}$

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

The intercept is calculated using:

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

Where

$(x_1,y_1) = (-2,13)$

$(x_2,y_2) = (0,y)$ --- we want to solve for y

So:

$\frac{1}{2} = \frac{y - 13}{0 --2}$

$\frac{1}{2} = \frac{y - 13}{2}$

Multiply both sides by 2

$1 =y - 13$

Make y the subject

$y =1 + 13$

$y = 14$

So, we have:

$m = -\frac{1}{4}$ and $b = 14$ -- for g(x)

$m = \frac{1}{2}$ and $y = 14$ --- for f(x)

By comparison:

The rate of change (i.e. slope) of f(x) is greater than that of g(x) because $1/2 > -1/2$

They have the same y intercept of 14