Question

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 2 multiplied by 1.5 to the power of x. The straight line f of x joins ordered pairs 3, 1 and 2, minus 1 and is extended on both sides. The straight line p of x joins the ordered pairs 1, 3 and 3, 1 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) (3, 1)

B) (3, 1), (2, -1)

C) (1, 3)

Explanation:

A) The problem statement tells you the point (3, 1) is on both lines.

B) The problem statement tells you the line goes through points ...

... (3, 1) and (2, -1).

C) The problem statement tells you point (1, 3) is a solution to p(x). It also happens that g(1) = 2·1.5¹ = 3, so (1, 3) is also a solution to g(x).

(1, 3) is a solution to p(x) = g(x) because p(1) = 3 = g(1).