MATH SOLVE

7 months ago

Q:
# 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 1, 1 and 3, negative 3 and is extended on both sides. The straight line p of x joins the ordered pairs 4, 2 and 2, negative 1 and is extended on both sides.Courtesy of Texas InstrumentsPart 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 g(x) = f(x)? Justify your answer. (4 points)

Accepted Solution

A:

Answer:Part A:The solution to the pair of equations represented by p(x) and f(x) is (2 , -1)Part B:(1 , 1) and (3 , -3) are the two solutions for f(x)Part C:The solution to the pair of equations represented by g(x) = f(x) is (0 , 3)Step-by-step explanation:* Lets study the three graphs- g(x) is an exponential function where f(x) = 2 + (1.5)^x- g(x) intersect the y-axis at point (0 , 3)- g(x) intersected f(x) at point (0 , 3)- f(x) is a linear function passing through point (3 , -3) , (1 , 1)- The slop of f(x) = 1 - -3/1 - 3 = 4/-2 = -2- f(x) intersect y-axis at point (0 , 3)- f(x) = -2x + 3- f(x) intersect x-axis at point (1.5 , 0)- f(x) intersected p(x) at point (2 , -1)- p(x) is a linear function passing through point (4 , 2) , (2 , -1)- The slop of p(x) = -1 - 2/2 - 4 = -3/-2 = 3/2- p(x) intersect y-axis at point (0 , -4)- p(x) = 3/2 x - 4- p(x) intersect x-axis at point (8/3 , 0)* Now lets solve the problem* Part A:∵ p(x) meet f(x) at point (2 , -1)∴ The solution to the pair of equations represented by p(x) and f(x) is (2 , -1)* Part B:∵ f(x) passing through (1 , 1) and (3 , -3)∴ (1 , 1) and (3 , -3) are the two solutions for f(x)∵ g(x) meet f(x) at point (0 , 3)∴ The solution to the pair of equations represented by g(x) = f(x) is (0 , 3)