Given : On a coordinate plane,a curved line with 3 arcs, lab led f of x, crosses the x-axis at (negative 2,0), (negative 1,0), (1,0), and (3,0) and the y axis at (0, negative 6).
To find: f when x = 0. i.e. f (0).
Solution: since the graph has 3 arcs and 4 solutions, it can be visualized as the follows: Between each solution, the function has to increase and decrease giving arcs in between. 1. One of the arcs is between (negative 2,0) and negative (1,0) 2. Second arc is between (negative 1,0) and (1,0) -this arc cuts the y axis, since x= 0 lies between x= -1 & x=1- 3. Third arc is between (1,0) and (3,0) Therefore only the 2nd arc cuts the y axis It’s given that the curve cuts the y axis at (0, -6) That is when x= 0, f(0) =-6 Therefore the value of f (0) is -6 only.
A simple matter of using Pythagoras. The hypotenuse is the ladder, and one of the legs is the wall, and we have to figure out the value of the other leg.
The Pythagorean formuda is (hypotenuse = a): a² + b² = c² (b and c are the other sides)
applying the values: a = 5 and b or c is 3 (I'll put b = 3)
The formula to find the area of a triangle is A = 1/2(b*h). Since we know the area already, we can substitute that value in to calculate the answer backwards.
