Solving Word Problems Involving Functions (3.7.3)

Question 1

• Function thinking allows you to solve a problem with two unknowns by setting up an equation with one unknown defined in terms of the other unknown. Then, when you can determine a value for the one unknown, you can solve for the other unknown.

Answer 1

• Function thinking allows you to solve a problem with two unknowns by setting up an equation with one unknown defined in terms of the other unknown. Then, when you can determine a value for the one unknown, you can solve for the other unknown.

Question 2

• f (x) means a function defined in terms of x. It also means the value an expression has for a given quantity, x.

Answer 2

• f (x) means a function defined in terms of x. It also means the value an expression has for a given quantity, x.

Question 3

For any rectangle, Perimeter = 2l + 2w ; Area = l · w

Answer 3

For any rectangle, Perimeter = 2l + 2w ; Area = l · w

Question 4

Once we know that the perimeter equals 50, we know
P = 50 = 2l + 2w
We can easily solve for w using this information. At any
specific length (l) we can now solve for the width (w).

Answer 4

Once we know that the perimeter equals 50, we know
P = 50 = 2l + 2w
We can easily solve for w using this information. At any
specific length (l) we can now solve for the width (w).

Question 5

Once we have a statement for w, we can define the area in terms of the other variable L. Our notation is A(L) which is read “area in terms of length,” or the function “A of L.”
Then, at any specific length, in this case when L = 5, we can calculate the area.

Answer 5

Once we have a statement for w, we can define the area in terms of the other variable L. Our notation is A(L) which is read “area in terms of length,” or the function “A of L.”
Then, at any specific length, in this case when L = 5, we can calculate the area.