The graph shows the functions f(x), p(x), and g(x): Graph of function f of x is y is equal to 2 plus the quantity 1.5 raised to the power of x. The straight line g of x joins ordered pairs negative 1, 7 and 1, negative 1 and is extended on both sides. The straight line p of x joins the ordered pairs 2, 0 and 4, 2 and is extended on both sides. Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by g(x) and p(x)? (3 points) Part B: Write any two solutions for p(x). (3 points) Part C: What is the solution to the equation g(x) = f(x)? Justify your answer. (4 points)

f(x)=2+1.5^x

g(x) is a str. line joining (1,7) and (1,-1) (you MUST use those parentheses)

p(x) = is a str. line joining the points (2,0) and (4,2)  (use those parentheses!)

Looking at g(x), we see that x does not change, but that y changes.  Thus, this is the straight vertical line whose x-coordinate is x=1.

Looking at p(x), we see that the slope, m, is (2/2), or 1, and that the equation is thus  y - 0 = 1(x-2), or y=x-2.

Determine where the lines representing p(x) and g(x) intersect:  Since g(x) is a vertical line with x=2, we set x=2 in y=x-2, obtaining y=0.

So the graphs of p(x) and g(x) intersect at (1,0).

There is no solution to p(x).  That's not an equation.  But if you set p(x)=0, you can solve for x:  0=x-2, or x=2.

Part C:  What is the solution to g(x)=f(x)?  In other words, where does f(x)=2+1.5^x intersect the vertical line x=1?  Set x=1 in f(x), obtaining f(x)=2+1.5^1, or f(x) = 2 + 1.5 = 3.5 (answer to C).