Question

(WILL GIVE YOU 30 POINTS!!!)

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

Graph of function g of x is y is equal to 3 multiplied by 1.2 to the power of x. The straight line f of x joins ordered pairs minus 3, minus 3 and 4, 4 and is extended on both sides. The straight line p of x joins the ordered pairs minus 6, 1 and minus 3, minus 3 and is extended on both sides.

Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)

Part B: Write any two solutions for f(x). (3 points)

Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)

Answer 1

(a) No solution

(b)

`(x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)`

(c)
`(-6,1)`

Explanation:

Given

See attachment for graph

Solving (a): Solution to p(x) and f(x)

Curve p(x) and line f(x) do not intersect.

So, there is no solution to the pair of p(x) and f(x)

Solving (b): Two solutions to f(x)

This means that we select any two point on straight line f(x)

From the line of f(x), we have:

`(x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)`

Solving (c): Solution to p(x) = g(x)

Here, we write out the point of intersection of p(x) and g(x)

From the graph, the point of intersection is:
`(-6,1)`