In the following graph , what is (g – f)(4)?

Question

In the graph shown, what is (g – f)(4)?

Grade 12 Advanced Functions

Please answer clearly and neatly. Thanks :)

Answer 1

Hi, the notation you used is a little strange. I'll assume you mean g(4) - f(4). In that notation, the value inside the parentheses is the x value, and the value we want is the y value at x=4. There are two straight lines on the graph, let's find the y values of each line when x=4.

For each line, the equation is going to go as f(x) = mx + b. If we find m and b, we can find f(x) anywhere!

m = slope of the line = (y2-y1)/(x2-x1). Plug in values of the points on the line, we get,

f(x) -> m = (4-0)/(8-(-8)) = 4/16 = 1/4

g(x) -> m = (7-(-7))/(6-(-1)) = 14/7 = 2

b = y-intercept (where does the line hit the y axis?)

f(x) -> b = 2

g(x) -> b = -5

Let's plug m and b into our functions!

f(x) = x/4 + 2

g(x) = 2x - 5

Now let's find f(4) and g(4)

f(4) = 4/4 + 2 = 3

g(4) = 2*4 - 5 = 3

Assuming I did all that correct, f(4) - g(4) = 0.