Question

The graph shows the functions f(x), p(x), and g(x):

Part A: What is the solution to the pair of equations represented by p(x) and f(x)?

Part B: Write any two solutions for f(x).

Part C: What is the solution to the equation p(x) = g(x)? Justify your answer.

Answer 1

The function f(x) is:

f(x)=x

This is because the line f(x) passes through the points (-1,-1), (0,0), (1,1) etc.

The function p(x) is:

p(x)=mx+C

Whereby (m) is the slope and (C) is a constant.

m=-4/3, as m=tan(ω)=O/A=-4/3 as slope is negative.

Now when y=-3, x=-3.

So:

-3=-4/3 *(-3) +C

-3= 4 + C

C=-7

This means that:

p(x)=-4/3x -7

Now, where p(x)=g(x), x=-6.

p(-6)=-4/3 * (-6) -7

p(-6)=24/3 -7

p(-6)=8-7

p(-6)=1

Therefore:

p(x) and g(x) meet at (-6, 1) and the solution to p(x)=g(x) is x=-6.