Solve the equation graphically to four decimal places.
-
A) No solution
B) 0.7922
C) 0.7922, 4.2078
D) 4.2078

Question

Solve the equation graphically to four decimal places.
-
A) No solution 
B) 0.7922 
C) 0.7922, 4.2078 
D) 4.2078

Quizplus · Accepted Answer

Firstly, graph both sides of the equation on the same coordinate plane.

The left side of the equation (y = sin(x)) is a known wave function that oscillates between -1 and 1.

The right side of the equation (y = x/3 + 0.5) is a linear function with a slope of 1/3 and a y-intercept of 0.5.

By inspecting the graph, it is clear that there are two points of intersection, one near x=0.79 and another near x=4.21.

Using the intersection tool on a graphing calculator or estimating the intersection points using the graph, we can see that the solution to the equation is x=0.7922 or x=4.2078.

Therefore, the best choice is C, which includes both of these intersection points. Without seeing the equation, we can tell that the answer involves two values because there are two x-intercepts. To solve the equation graphically, plot the function and see where it crosses the x-axis. The point(s) of intersection give the solution(s). Using a graphing calculator or software, we can plot the function y = sin(x) + 2x - 1 and find that it intersects the x-axis at approximately x= 0.7922 and x = 4.2078. Therefore, the answer is choice C.

Solve the Equation Graphically to Four Decimal Places