Jessie and Laura are trying to compute the area of a triangle with base 5cm and height, h. Jessie multiplies 1/2 by the product of 5 and h, while Laura multiplies 5 by h and then takes half the result.
a)Let J(h) be the function defined by Jessie's expression and L(h) be the function defined by Laura. Write expressions that define each function.
b)Are their functions equivalent? Justify answer by using definition of equivalent functions.
they are the same, since multiplication is commutative.
a)
1) Jessie's function, J(h), is defined by multiplying 1/2 by the product of 5 and h:
J(h) = (1/2) * 5h
2) Laura's function, L(h), is defined by multiplying 5 by h and then taking half the result:
L(h) = (1/2) * 5h
b) Yes, their functions are equivalent. We can see this by simplifying both functions:
1) Jessie's function (J(h)):
J(h) = (1/2) * 5h = (5/2)h
2) Laura's function (L(h)):
L(h) = (1/2) * 5h = (5/2)h
Both functions simplify to (5/2)h, which means they are equivalent. The fact that they have the same simplified form shows that they produce the same output for any given value of h. Therefore, their functions are equivalent.